ENGLISH

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

By Yaroslav Chabanyuk , Anatolii Nikitin , Uliana Khimka

Book information

Publisher
Wiley-ISTE
Year
2020
ISBN
1786305569, 9781786305565
Language
english
Format
EPUB
Filesize
23 MB (23795173 bytes)
Series
Mathematics and Statistics
Pages
240\0
Time added
2022-09-24 10:40:56

Description

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.

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