Authors: D. Koroliouk, I. Samoilenko

Summary: This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investi­gated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.

ISBN 978-1-786-30911-2

Available at: https://www.iste.co.uk/book. php?id=2030

Responsible institutions: Institute of Mathematics of the NAS of Ukraine

Published: London : ISTEWILEY

Size in pages: 260