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

Yaroslav Chabanyuk

ISBN 10: 1786305569 / ISBN 13: 9781786305565

Published by ISTE Ltd and John Wiley & Sons Inc, 2020

About this Item

2020. 1st Edition. Hardcover. . . . . .

Seller Inventory # V9781786305565

Bibliographic Details

• Title: Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi-Markov Switching Using Approximation Schemes
• Publisher: ISTE Ltd and John Wiley & Sons Inc
• Publication Date: 2020
• Language: English
• ISBN 10: 1786305569
• ISBN 13: 9781786305565
• Binding: Hardcover
• Edition: 1st Edition
• Condition: New

About this title

Synopsis

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.

About the Author

Yaroslav Chabanyuk is Senior Research Officer at Lublin University of Technology, Poland, and at Ivan Franko National University of Lviv, Ukraine. His work specializes in system analysis and properties of random processes with Markov and semi-Markov switching.

Anatolii Nikitin is Senior Research Officer at Taras Shevchenko National University of Kyiv, Ukraine, and Professor at the Jan Kochanowski University (JKU) in Kielce, Poland. His work specializes in system analysis and asymptotic properties of stochastic differential equations.

Uliana Khimka is Professor at Ivan Franko National University of Lviv. She is the author of more than 100 scientific works and, in 2013, she defended her PhD thesis, Continuous Stochastic Optimizations Procedure in the Environment with Markov Switching.