Random perturbation methods with applications in science and engineering
type: Item
instance of: scholarly article
title: Random perturbation methods with applications in science and engineering
zbMATH Open document ID: 0998.37001
author: Habib Salehi
author: Anatolii V. Skorokhod
author: Frank Hoppensteadt
published in: Applied Mathematical Sciences
publication date: 2002-09-10T00:00:00Z
review text: The book studies random perturbations of various deterministic models appearing in applications. The book starts with an Introduction and two general chapters about ergodic theorems and convergence properties of stochastic processes. The third chapter deals with the averaging method applied to the Volterra integral equation, ordinary differential equations and difference equations. The last section of this chapter deals with large deviations. The next chapter deals with normal deviations and Chapter 5 studies diffusion approximations. Chapter 6 deals with stability properties of systems, in particular, with respect to jump type perturbations. Other topics considered there are the stochastic resonance and random perturbations of difference equations. In Chapter 7 the authors study Markov chains with random transition probabilities, in particular, Markov chains with randomly perturbed probabilities. Chapter 8 deals with randomly perturbed mechanical (Hamiltonian) systems and Chapter 9 concerns with dynamical systems on a torus and their random perturbations. The last three chapters deal with phase-locked loops, models of population biology and genetics, respectively.
reviewed by: Yuri Kifer
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 70K65
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1798928
zbMATH Keywords: random perturbations
zbMATH Keywords: averaging
zbMATH Keywords: diffusion approximation
MaRDI profile type: Publication
full work available at URL: b98905
OpenAlex ID: W4300140424
DOI: 10.1007/B98905
description: scientific article; zbMATH DE number 1798928