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.

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

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Hardback by Yaroslav Chabanyuk , Anatolii Nikitin

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This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are... Read more

    Publisher: ISTE Ltd and John Wiley & Sons Inc
    Publication Date: 18/12/2020
    ISBN13: 9781786305565, 978-1786305565
    ISBN10: 1786305569

    Number of Pages: 240

    Non Fiction , Mathematics & Science , Education

    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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