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In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

In this paper we give an $L_p$-theory for stochastic parabolic equations with random fractional Laplacian operator. The driving noises are general L\'evy processes.

These notes are an introduction to the theory of stochastic processes based on several sources. The presentation mainly follows the books of van Kampen and Wio, except for the introduction, which is taken from the book of Gardiner and the parts devoted to the Langevin equation and the methods for solving Langevin and Fokker-Planck equations, which are based on the book of Risken.

This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school and which are usually written in French. The material presented in the last three chapters is less standard and takes into account some recent developments.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n or =0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t = 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Z(t), the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur; that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.

Bell System Technical Journal, 40: 3. May 1961 pp 795-820. Stochastic Processes with Balking in the Theory of Telephone Traffic. (Takacs, Lajos)

Bell System Technical Journal, 40: 3. May 1961 pp 795-820. Stochastic Processes with Balking in the Theory of Telephone Traffic. (Takacs, Lajos)

Bell System Technical Journal, 40: 3. May 1961 pp 795-820. Stochastic Processes with Balking in the Theory of Telephone Traffic. (Takacs, Lajos)

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Delhi College Of Engineering Date Accessioned: 8/8/2015 19:57 The Digital Library of India was a project under the auspices of the Government of India.