Random perturbation methods with applications in science and engineering
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.
scientific article; zbMATH DE number 1798928