Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi-Markov Switching Using Approximation Schemes

Chabanyuk, Yaroslav and Nikitin, Anatolii and Khimka, Uliana (2020) Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi-Markov Switching Using Approximation Schemes. Wiley-ISTE. ISBN 9781786305565

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Abstract

This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are investigated under the conditions of classical and non-classical (Levy and Poisson) approximations in addition to jumping stochastic approximations and continuous optimization procedures.

Among other asymptotic properties, particular attention is given to weak convergence, dissipativity, stability and the control of processes and their generators.

Weak convergence of stochastic processes is usually proved by verifying two conditions: the tightness of the distributions of the converging processes, which ensures the existence of a converging subsequence, and the uniqueness of the weak limit. Achieving the limit can be done on the semigroups that correspond to the converging process as well as on appropriate generators. While this provides the convergence of generators, a natural question arises concerning the uniqueness of a limit semigroup.

Item Type:	Book
Subjects:	by fields of science > Mathematics
Divisions:	The College of Economics Management > Department of Economic-Mathematical Modeling and Information Technologies
Depositing User:	Anatolii Nikitin
Date Deposited:	08 May 2024 11:20
Last Modified:	08 May 2024 11:20
URI:	https://eprints.oa.edu.ua/id/eprint/9072

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