Random Evolutionary Systems

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 ixIntroduction xiChapter 1. Basic Tools for Asymptotic Analysis 1Chapter 2. Weak Convergence in Poisson and Lévy Approximation Schemes 57Chapter 3. Large Deviations in the Scheme of Asymptotically Small Diffusion 107Chapter 4. Large Deviations of Systems in Poisson and Lévy Approximation Schemes 119Chapter 5. Large Deviations of Systems in the Scheme of Splitting and Double Merging 149Chapter 6. Difference Diffusion Models with Equilibrium 169Chapter 7. Random Evolutionary Systems in Discrete–Continuous Time 223Chapter 8. Diffusion Approximation of Random Evolutions in Random Media 239References 279Index 287