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Random Evolutionary Systems
Asymptotic Properties and Large Deviations
Dmitri Koroliouk (Author), Igor Samoilenko (Author)
9781786307521, Wiley
Hardback, published 19 November 2021
320 pages
1 x 1 x 1 cm, 0.454 kg
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.
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
Subject Areas: Mathematics [PB]
