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xvii, 746 p. 23 cm

xvii, 746 p. 23 cm

xvii, 746 pages 23 cm

xvii, 746 pages 23 cm

Some problems in the filtering and the detection of diffusion processes that are solutions of stochastic differential equations are studied. Transition densities for Markov process solutions of a large class of stochastic differential equations are shown to exist and to satisfy Kolmogorov's equations. These results extend previously known results by allowing the drift coefficient to be unbounded. With these results for transition densities the nonlinear filtering problem is discussed and the conditional probability of the state vector of the system conditioned on all the past observations is shown to exist and a stochastic equation is derived for the evolution in time of the conditional probability density. A stochastic differential equation is also obtained for the conditional moments. These derivations use directly the continuous time processes. Necessary conditions that coincide with the previously known sufficient conditions for the absolute continuity of measures corresponding to solutions of stochastic differential equations are obtained. Applications are made to the detection of one diffusion process in another. Previous results on the relation between detection and filtering problems are rigorously obtained and extended.

Some problems in the filtering and the detection of diffusion processes that are solutions of stochastic differential equations are studied. Transition densities for Markov process solutions of a large class of stochastic differential equations are shown to exist and to satisfy Kolmogorov's equations. These results extend previously known results by allowing the drift coefficient to be unbounded. With these results for transition densities the nonlinear filtering problem is discussed and the conditional probability of the state vector of the system conditioned on all the past observations is shown to exist and a stochastic equation is derived for the evolution in time of the conditional probability density. A stochastic differential equation is also obtained for the conditional moments. These derivations use directly the continuous time processes. Necessary conditions that coincide with the previously known sufficient conditions for the absolute continuity of measures corresponding to solutions of stochastic differential equations are obtained. Applications are made to the detection of one diffusion process in another. Previous results on the relation between detection and filtering problems are rigorously obtained and extended.

un libro para iniciar en probabilidad

un libro para iniciar en probabilidad

un libro para iniciar en probabilidad

un libro para iniciar en probabilidad

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

Many aspects of signal processing and communication theory have proven to be limited by a lack of sufficient developments in the areas of probability theory and mathematical statistics. Our investigations attempted to overcome this deficiency by contributing both to the underlying theoretical basis of the area as well as to some applied aspects of the area, and we have obtained a large body of results. Some principal thrust areas of our research effort have been concerned with quantization theory, signal detection, and estimation theory. A brief topical overview of our research areas follows. Quantization - existence of optimal quantizers, convergence properties of sequences of quantizers, design of quantizers, Signal detection - effects of statistical dependence, relative efficiency between detectors, nonparametric detection, Estimation - effects of imperfect data, a general class of fidelity criteria leading to nonlinear estimators, convergence properties of sequences of estimators; and Additional areas - meadian filters; stability of differential equations with random coefficients; bandwidth properties of random processes; contention resolution in local area computer networks; image compression; counterexamples.

This interim report constitutes a summary of research performed under the grant during this period. First the author presents a list of personnel involved in the research effort. In the next section the author presents a summary of research results that have been achieved. Then in the following section the author briefly comments upon the research in progress. This is followed by a list of publications supported during this grant year. Most research results are in the areas of quantization theory and detection theory. Quantization is the process by which data is reduced to a simpler, more coarse representation which is more compatible with digital processing. Loosely speaking, quantization is the heart of analog to digital conversion. It is an area which has increased in importance in the last few years due to the burgeoning advances in digital technology. The typical goal of quantization is to reduce data to a simplier representation without causing much distortion; that is, the output of a quantizer should be close to the input, with some appropriate measure of distance. Another research area in which we have recently obtained results is the area of signal detection. The detection problem is modeled as a test between two statistical hypotheses; we assume that under the null hypothesis noise alone is being observed, and under the alternate hypothesis a signal plus noise is being observed. We considered discrete time detection.