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1Stochastic Processes

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2Stochastic Processes And Their Applications 2003: Vol 105 Index

Stochastic Processes and Their Applications 2003: Volume 105 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_2003-04_104_2_0 . Next issue: sim_stochastic-processes-and-their-applications_2003-05_105_1_0 .

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3Models For Behavior : Stochastic Processes In Psychology

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Stochastic Processes and Their Applications 2003: Volume 105 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_2003-04_104_2_0 . Next issue: sim_stochastic-processes-and-their-applications_2003-05_105_1_0 .

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4BSP 2014 - Introduction To Applied Probability And Stochastic Processes

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Trimester 2 2018/2019

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5Stochastic_processes_sec3

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6The Stochastic Modeling Of Elementary Psychological Processes

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7Stochastic Processes In Polymeric Fluids : Tools And Examples For Developing Simulation Algorithms

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8Stationary And Related Stochastic Processes; Sample Function Properties And Their Applications

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9Stochastic Processes : A Festschrift In Honor Of Gopinath Kallianpur

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10DTIC ADA073846: Long-Term Distributions Of Stochastic Processes With Application To Ship Hull Stress Statistics.

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The mathematical properties of the following probability distributions and their moment generating functions are derived: Weibull distribution; Rayleigh distribution; Exponential distribution; Normal distribution; Voznesensky distribution; and Generalized Rayleigh distribution. The relative merits of applying these distributions to problems in ship responses to the sea, which is described as a stationary stochastic process, are discussed. In Part 2, the most promising long-term distributions derived from the above survey are applied to ship bending stress data from four ships. It is concluded that a numerical solution of long-term distributions, using either Weibull or Normal distributions of the short-term Rayleigh parameters (classified by weather groups) is better than any explicit functions. (Author)

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11MIT 6.262 Discrete Stochastic Processes, Spring 2011

Lecture videos from 6.262 Discrete Stochastic Processes, Spring 2011. View the complete course: http://ocw.mit.edu/6-262S11 Instructor: Robert Gallager License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms

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12Stochastic Processes And Their Applications 1993: Vol 48 Index

Stochastic Processes and Their Applications 1993: Volume 48 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1993-09_47_2 . Next issue: sim_stochastic-processes-and-their-applications_1993-10_48_1 .

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13Seminar On Stochastic Processes, 1982

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Stochastic Processes and Their Applications 1993: Volume 48 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1993-09_47_2 . Next issue: sim_stochastic-processes-and-their-applications_1993-10_48_1 .

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14Seminar On Stochastic Processes, 1985

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322p. ; 24 cm

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15An Introduction To Stochastic Processes With Applications To Biology

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16Introduction To Stochastic Processes In Biostatistics

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322p. ; 24 cm

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17Stochastic Processes And Their Applications 1997: Vol 68 Index

Stochastic Processes and Their Applications 1997: Volume 68 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1997-05-16_67_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1997-05-30_68_1_0 .

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18Stochastic Processes And Their Applications 1993: Vol 44 Index

Stochastic Processes and Their Applications 1993: Volume 44 , Issue Index. Digitized from IA1653419-05 . Next issue: sim_stochastic-processes-and-their-applications_1993-01_44_1 .

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19The Analysis Of Stochastic Processes Using GLIM

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20Stochastic Processes In Mathematical Physics And Engineering : [proceedings Of A Symposium In Applied Mathematics Of The American Mathematical Society : Held In New York City, April 30-May 2, 1963

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21Statistics And Control Of Stochastic Processes : Seminar : Papers

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22Stable Non-Gaussian Random Processes : Stochastic Models With Infinite Variance

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23Applied Probability And Stochastic Processes

Applied Probability and Stochastic Processes Richard M. Feldman · Ciriaco Valdez-Flores Second Edition Springer-Verlag Berlin Heidelberg 2010

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24Stochastic Models For Social Processes

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Bibliography: p. 381-402

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25DTIC ADA147863: Infinite Order Autoregressive Representations Of Multivariate Stationary Stochastic Processes.

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While it is well-known that every purely nondeterministic full rank q- variate weakly stationary stochastic process (X sub n) with the spectral density W has an (infinite order) one-sided moving average representation, not every such process can have a mean convergent (infinite order) autoregressive representation (ARR) and the problem of ARR of such processes has not received the attention which it deserves. Due to the importance of ARR in prediction theory, and particularly in the statistical theory of multivariate time series, this paper is devoted to the problem of finding the weakest condition on W which guarantees the existence of an infinite order ARR for (X sub n).

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26DTIC ADA480737: Stochastic Simulations Of Cellular Biological Processes

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INTRODUCTION: From a systems engineering point of view, cells consist of a complex set of nested, nonlinear control systems dominated by feed-back and feed-forward loops. The more complex the system is, the more important are the issues concerning the robustness and parameter optimization, therefore modeling and simulations are important for both engineering and reverse-engineering of biosystems. OBJECTIVE: At the functional level, all biological processes in cells can be represented as a series of biochemical reactions. Since such reactions are stochastic in nature, the user must run thousands of simulations to characterize the ensemble behavior of biological systems. We developed a software package called Biomolecular Network Simulator (BNS) to model and simulate complex biomolecular reaction networks using High Performance Computing (HPC). METHODOLOGY: The Biomolecular Network Simulator uses the Gillespie stochastic algorithm to simulate the evolution of a system of biochemical reactions. The BNS code is a combination of MATLAB and C-coded modules. This combination allows one to use the interactive features and visualization tools of MATLAB, while achieving high speed for the computationally intensive part of the software. The software is parallelized with the MPI library to run on multiprocessor architectures. RESULT: The Biomolecular Network Simulator consists of two sets of tools: for simulations of the system and for the analysis of simulation results. The Graphical User Interface of BNS allows users to easily set parameters for the model and simulations and to select analysis method. Multiple types of post-simulation analyses are available. SIGNIFICANCE TO DoD: The Developed software allows DoD scientists to build, simulate and analyze complex cellular biomolecular networks utilizing the capacities of HPC. It provides the foundational capability to design and integrate biological constructs into a new generation of biotechnology products.

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27Stochastic Processes And Their Applications 1989: Vol 32 Index

Stochastic Processes and Their Applications 1989: Volume 32 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1989-04_31_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1989-06_32_1_0 .

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28Stochastic Processes And Their Applications 1991: Vol 37 Index

Stochastic Processes and Their Applications 1991: Volume 37 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1990-12_36_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1991-02_37_1_0 .

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29Stochastic Processes And Their Applications 1993: Vol 46 Index

Stochastic Processes and Their Applications 1993: Volume 46 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1993-04_45_2 . Next issue: sim_stochastic-processes-and-their-applications_1993-05_46_1 .

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30Stochastic Processes And Their Applications 1994: Vol 49 Index

Stochastic Processes and Their Applications 1994: Volume 49 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1993-11_48_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1994-01_49_1_0 .

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31Stochastic Processes And Their Applications 1994: Vol 51 Index

Stochastic Processes and Their Applications 1994: Volume 51 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1994-04_50_2 . Next issue: sim_stochastic-processes-and-their-applications_1994-06_51_1 .

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32Stochastic Processes And Their Applications 1996: Vol 62 Index

Stochastic Processes and Their Applications 1996: Volume 62 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1996-02_61_2 . Next issue: sim_stochastic-processes-and-their-applications_1996-03_62_1 .

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33DTIC ADA256788: Spectral Multiplicity For Second-Order Stochastic Processes

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The theory of spectral multiplicity for second-order stochastic processes is developed from first principles. Each of the representations originally obtained by Cramer and by Hida is developed. The Hellinger-Hahn theorem on multiplicity in Hilbert space is obtained as a corollary, instead of being used to provide the representations.

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34Stochastic Processes And Their Applications 1988: Vol 29 Index

Stochastic Processes and Their Applications 1988: Volume 29 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1988-06_28_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1988-08_29_1_0 .

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35Stochastic Processes And Their Applications 1991: Vol 37 Index

Stochastic Processes and Their Applications 1991: Volume 37 , Issue Index. Digitized from IA1653419-02 . Previous issue: sim_stochastic-processes-and-their-applications_1990-12_36_2 . Next issue: sim_stochastic-processes-and-their-applications_1991-02_37_1 .

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36Stochastic Processes And Their Applications 1991: Vol 38 Index

Stochastic Processes and Their Applications 1991: Volume 38 , Issue Index. Digitized from IA1653419-02 . Previous issue: sim_stochastic-processes-and-their-applications_1991-04_37_2 . Next issue: sim_stochastic-processes-and-their-applications_1991-06_38_1 .

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37Stochastic Processes And Their Applications 1992: Vol 41 Index

Stochastic Processes and Their Applications 1992: Volume 41 , Issue Index. Digitized from IA1653419-02 . Previous issue: sim_stochastic-processes-and-their-applications_1992-03_40_2 . Next issue: sim_stochastic-processes-and-their-applications_1992-05_41_1 .

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38Stochastic Processes And Their Applications 1994: Vol 52 Index

Stochastic Processes and Their Applications 1994: Volume 52 , Issue Index. Digitized from IA1652405-03 . Previous issue: sim_stochastic-processes-and-their-applications_1994-07_51_2_0 . Next issue: sim_stochastic-processes-and-their-applications_1994-08_52_1_0 .

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39Stochastic Processes And Their Applications 1995: Vol 59 Index

Stochastic Processes and Their Applications 1995: Volume 59 , Issue Index. Digitized from IA1653419-05 . Previous issue: sim_stochastic-processes-and-their-applications_1995-08_58_2 . Next issue: sim_stochastic-processes-and-their-applications_1995-09_59_1 .

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40Time Parameters And Lorentz Transformations Of Relativistic Stochastic Processes

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Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell distribution, the associated proper-time parameterized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.

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41Non-equilibrium Dynamics Of Stochastic Point Processes With Refractoriness

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Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.

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42On The Excursions Of Reflected Local Time Processes And Stochastic Fluid Queues

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This paper extends previous work by the authors. We consider the local time process of a strong Markov process, add negative drift, and reflect it \`a la Skorokhod. The resulting process is used to model a fluid queue. We derive an expression for the joint law of the duration of an excursion, the maximum value of the process on it, and the time distance between successive excursions. We work with a properly constructed stationary version of the process. Examples are also given in the paper.

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43Hidden Symmetries And Equilibrium Properties Of Multiplicative White-noise Stochastic Processes

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Multiplicative white-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassman formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taken into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.

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44Pathwise Stochastic Integration With Finite Variation Processes Uniformly Approximating Càdlàg Processes

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For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on compacts. The application of the defined class is the definition of stochastic integral with semimartingale integrand and integrator as a limit of pathwise Lebesgue-Stieltjes integrals. This construction leads to the stochastic integral with some correction term (different from the Stratonovich integral). We compare the obtained result with classical results of Wong-Zakai and Bichteler on pathwise stochastic integration. As a "byproduct" we obtain an example of a series of double Skorohod maps of a standard Brownian motion, which is not a semimartingale.

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45Differential Equation Approximations Of Stochastic Network Processes: An Operator Semigroup Approach

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The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs that depends on the state space size ($N$) and can be written as $\dot u_N=A_N u_N$. Our results rely on the convergence of the transition matrices $A_N$ to an operator $A$. This convergence also implies that the solutions $u_N$ converge to the solution $u$ of $\dot u=Au$. The limiting ODE can be easily used to derive simpler mean-field-type models such that the moments of the stochastic process will converge uniformly to the solution of appropriately chosen mean-field equations. A bi-product of this method is the proof that the rate of convergence is $\mathcal{O}(1/N)$. In addition, it turns out that the proof holds for cases that are slightly more general than the usual density dependent one. Moreover, for Markov chains where the transition rates satisfy some sign conditions, a new approach for proving convergence to the mean-field limit is proposed. The starting point in this case is the derivation of a countable system of ordinary differential equations for all the moments. This is followed by the proof of a perturbation theorem for this infinite system, which in turn leads to an estimate for the difference between the moments and the corresponding quantities derived from the solution of the mean-field ODE.

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46On The Finite Dimensional Joint Characteristic Function Of L\'{e}vy's Stochastic Area Processes

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs that depends on the state space size ($N$) and can be written as $\dot u_N=A_N u_N$. Our results rely on the convergence of the transition matrices $A_N$ to an operator $A$. This convergence also implies that the solutions $u_N$ converge to the solution $u$ of $\dot u=Au$. The limiting ODE can be easily used to derive simpler mean-field-type models such that the moments of the stochastic process will converge uniformly to the solution of appropriately chosen mean-field equations. A bi-product of this method is the proof that the rate of convergence is $\mathcal{O}(1/N)$. In addition, it turns out that the proof holds for cases that are slightly more general than the usual density dependent one. Moreover, for Markov chains where the transition rates satisfy some sign conditions, a new approach for proving convergence to the mean-field limit is proposed. The starting point in this case is the derivation of a countable system of ordinary differential equations for all the moments. This is followed by the proof of a perturbation theorem for this infinite system, which in turn leads to an estimate for the difference between the moments and the corresponding quantities derived from the solution of the mean-field ODE.

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47Half-Region Depth For Stochastic Processes

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We study the concept of half-region depth, introduced by Lopez-Pintado and Romo in 2011. We show that for a wide variety of standard stochastic processes, such as Brownian motion and other symmetric stable processes with stationary independent increments tied down at 0, half-region depth assigns depth zero to all sample functions. To alleviate this difficulty we introduce a method of smoothing, which often not only eliminates the problem of zero depth, but allows us to extend the theoretical results on consistency in that paper up to the $\sqrt n$ level for many smoothed processes.

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48Approximations Of Fractional Stochastic Differential Equations By Means Of Transport Processes

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We present strong approximations with rate of convergence for the solution of a stochastic differential equation of the form $$ dX_t=b(X_t)dt+\sigma(X_t)dB^H_t, $$ where $b\in C^1_b$, $\sigma \in C^2_b$, $B^H$ is fractional Brownian motion with Hurst index $H$, and we assume existence of a unique solution with Doss-Sussmann representation. The results are based on a strong approximation of $B^H$ by means of transport processes of Garz\'on et al (2009). If $\sigma$ is bounded away from 0, an approximation is obtained by a general Lipschitz dependence result of R\"omisch and Wakolbinger (1985). Without that assumption on $\sigma$, that method does not work, and we proceed by means of Euler schemes on the Doss-Sussmann representation to obtain another approximation, whose proof is the bulk of the paper.

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49Generators Of Some Non-commutative Stochastic Processes

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A fundamental result of Biane (1998) states that a process with freely independent increments has the Markov property, but that there are two kinds of free Levy processes: the first kind has stationary increments, while the second kind has stationary transition operators. We show that a process of the first kind (with mean zero and finite variance) has the same transition operators as the free Brownian motion with appropriate initial conditions, while a process of the second kind has the same transition operators as a monotone Levy process. We compute an explicit formula for the generators of these families of transition operators, in terms of singular integral operators, and prove that this formula holds on a fairly large domain. We also compute the generators for the $q$-Brownian motion, and for the two-state free Brownian motions.

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50Stochastic Dynamics Of Two-step Processes With Harmonic Potential

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In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a certain instant of time (say,$tau$), when a restoring force is applied to bring them back to some point in configuration space. The physical quantities of interest that have been studied are the Survival Probability and the First Passage distribution for return to the specified target point. We observe nontrivial dependence of these quantities on $tau$ as well as on the width of the initial distribution, which has been taken to be Gaussian in position and velocity.

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