Asymptotic and Analytic Approaches in Random Evolutionary Systems

Author: Dmitri Koroliouk

This book delves into the application of various asymptotic and analytic techniques to study random evolutionary systems. It presents a comprehensive analysis of typical problems using specific examples, employing constructive mathematical models that closely resemble natural processes. These models are more accurate in describing the trajectories of diffusion-type processes compared to the Wiener process.

Markov Evolutionary System

The Markov evolutionary system is one of the models explored in the book. In this system, the time during which a particle moves towards a particular direction is exponentially distributed with an intensity parameter. This model effectively describes the motion of particles with a finite speed, mirroring the characteristics of a natural physical process, including free run and finite propagation speed.

Semi-Markov Evolutionary System

Another model discussed in the book is the semi-Markov evolutionary system. This model features an arbitrary distribution of the switching process, further enhancing the realism of the particle motion depiction. The number of possible directions of evolution in these models can be either finite or infinite, providing a nuanced understanding of complex systems.

Publication Details:
Publisher: Wiley
Publication Date: July 18, 2023
Language: English
ISBN: 9781786309112, 9781394229468