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.
Table of Contents
1. Basic Tools for Asymptotic Analysis.2. Weak Convergence in Poisson and Lévy Approximation Schemes.
3. Large Deviations in the Scheme of Asymptotically Small Diffusion.
4. Large Deviations of Systems in Poisson and Lévy Approximation Schemes.
5. Large Deviations of Systems in the Scheme of Splitting and Double Merging.
6. Difference Diffusion Models with Equilibrium.
7. Random Evolutionary Systems in Discrete-Continuous Time.
8. Diffusion Approximation of Random Evolutions in Random Media.
