Random Evolutionary Systems

Asymptotic Properties and Large Deviations

Dmitri Koroliouk, Igor Samoilenko (Autoren)

Buch | Hardcover

320 Seiten

2021
ISTE Ltd and John Wiley & Sons Inc (Verlag)
978-1-78630-752-1 (ISBN)

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Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asymptotic properties and large deviations. In Random Evolutionary Systems we consider these systems in terms of the operators that appear in the schemes of their diffusion and the Poisson approximation. Such an approach allows us to obtain a number of limit theorems and asymptotic expansions of processes that model complex stochastic systems, both those that are autonomous and those dependent on an external random environment. In this case, various possibilities of scaling processes and their time parameters are used to obtain different limit results.

Dmitri Koroliouk is a Doctor of Sciences (Hab.), leading researcher at the Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine, and Professor at the National Technical University of Ukraine, "Igor Sikorsky Kyiv Polytechnic Institute". He is the author of 80 scientific publications and also holds 10 European patents for industrial inventions. Igor Samoilenko is a Doctor of Sciences (Hab.) and Associate Professor at the Faculty of Computer Science and Cybernetics at the Taras Shevchenko National University of Kyiv, Ukraine. He is the author of 60 scientific publications.

Preface ix

Introduction xi

Chapter 1. Basic Tools for Asymptotic Analysis 1

Chapter 2. Weak Convergence in Poisson and Lévy Approximation Schemes 57

Chapter 3. Large Deviations in the Scheme of Asymptotically Small Diffusion 107

Chapter 4. Large Deviations of Systems in Poisson and Lévy Approximation Schemes 119

Chapter 5. Large Deviations of Systems in the Scheme of Splitting and Double Merging 149

Chapter 6. Difference Diffusion Models with Equilibrium 169

Chapter 7. Random Evolutionary Systems in Discrete–Continuous Time 223

Chapter 8. Diffusion Approximation of Random Evolutions in Random Media 239

References 279

Index 287

Erscheinungsdatum	22.10.2021
Verlagsort	London
Sprache	englisch
Maße	10 x 10 mm
Gewicht	454 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Naturwissenschaften ► Biologie
ISBN-10	1-78630-752-9 / 1786307529
ISBN-13	978-1-78630-752-1 / 9781786307521
Zustand	Neuware