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Full Description
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.
Contents
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
