Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms

This book provides asymptotic and analytic approaches for studying random evolutionary systems,using constructive mathematical models to describe natural processes. It examines models with particles having free distance between collisions,including Markov and semi-Markov systems with finite or infinite possible directions of evolution.

Format: Hardback
Length: 272 pages
Publication date: 24 August 2023
Publisher: ISTE Ltd and John Wiley & Sons Inc

This captivating book delves into a diverse range of asymptotic and analytic approaches, applied to the study of random evolutionary systems. It explores a multitude of typical problems, tailored to specific examples, utilizing constructive mathematical models to depict natural processes with greater realism. These models specifically capture the trajectories of diffusion-type processes, surpassing the limitations of the Wiener process.

We delve into models where particles possess a certain degree of freedom between consecutive collisions. Simultaneously, we examine two distinct cases: the Markov evolutionary system, characterized by the exponential distribution of time spent moving towards a particular direction, with an intensity parameter λ; and the semi-Markov evolutionary system, where the switching process follows an arbitrary distribution.

By investigating these models, we gain insights into the motion of particles with finite speed and the proposed random evolutionary process, exhibiting characteristics akin to natural physical processes: a free run and finite propagation speed. The proposed models allow for the possibility of a finite or infinite number of possible directions of evolution.

This comprehensive exploration showcases the power of mathematical models in elucidating complex phenomena, offering valuable insights into the dynamics of random evolutionary systems and their applications in various fields.

Weight: 662g
ISBN-13: 9781786309112