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Stochastic Geometry and Wireless Networks. Now Publishers Inc. Martingale Methods in Financial Modelling. Shreve Random Processes. A Festschrift for Herman Rubin. The Mathematical Gazette. Snyder; Michael I. Miller Random Point Processes in Time and Space. Some History of Stochastic Point Processes". International Statistical Review. Basic Principles and Applications of Probability Theory. Foundations of Modern Probability. Stochastic processes: a survey of the mathematical theory. Adler; Jonathan E. Taylor Random Fields and Geometry. Lawler; Vlada Limic Random Walk: A Modern Introduction.

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World Scientific Publishing Co Inc. Kloeden; Eckhard Platen Numerical Solution of Stochastic Differential Equations. Oxford English Dictionary 3rd ed. September Subscription or UK public library membership required. Theory of probability and statistics as exemplified in short dictums. NG Verlag. Alexandr A. Chuprov: Life, Work, Correspondence. Bibcode : PNAS Mathematische Annalen. Fristedt; Lawrence F.

Gray A Modern Approach to Probability Theory. Applied Probability and Queues. Stochastic Processes and Models. Gubner Essentials of Stochastic Processes.

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Probability Theory: A Comprehensive Course. Probability: Theory and Examples. Encyclopedia of Statistical Sciences. Probability: A Graduate Course. Probability and Random Processes. Archive for History of Exact Sciences. Brownian Motion and Stochastic Calculus. Continuous Martingales and Brownian Motion.

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## Almost Periodic Stochastic Processes

Rozanov Markov Random Fields. Ross Tweedie Markov Chains and Stochastic Stability. Proof The proofs of i and ii follow along the lines as for general almost periodic functions with values in a Banach space, and hence omitted. To prove iii , we combine both Chebychev inequality and ii to obtain.

Suppose that F is Lipschitzian in the following sense:. In this section we make extensive use of the results of the previous section to study the existence and uniqueness of a square-mean almost periodic solution to the class of stochastic differential equation. Definition 3.

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Indeed, assuming that X is square-mean almost periodic and using H1 and Theorem 2. Similarly, assuming that X is square-mean almost periodic and using H2 and Theorem 2. Of course, this is more complicated than the previous case because of the involvement of the Brownian motion W. Note that W is also a Brownian motion and has the same distribution as W. To complete the proof, it suffices to prove that L has a unique fixed-point. References [1] Arnold, L. Stochastics and Stochastic Reports, 64, — Stochastic Analaysis and Applications, 13 1 , 13— Statistics and Probability: Essays in Honor of C.

Rao, pp. Journal of Computational and Applied Mathematics, 1 , 87— Georgian Mathematical Journal, 3 3 , — Stochastics and Stochastic Reports, 38, — Union Jap. Read Free For 30 Days. Existence of almost periodic solutions. Flag for inappropriate content. Related titles. Carousel Previous Carousel Next. Mathematical Methods in Quantum Mechanics - G. Jump to Page. Search inside document. Applicable Analysis Vol.

This chapter also offers an introduction to the mathematical theory of stochastic processes, including the notion of continuity, measurability, stopping times, martingales,Wiener processes, and Gaussian processes. An investigation on stochastic differential equations driven by Wiener processes is given at end of the chapter.

## Almost Periodic Stochastic Processes / Edition 1

Special emphasis will be on the boundedness and stability of solutions. Springer Professional. Back to the search result list.