Introduction * Ergodic Theorems * Convergence Properties of Stochastic Processes * Averaging * Normal Deviation * Diffusion Approximation * Stability * Markov Chains with Random Transition Probabilities * Randomly Perturbed Mechanical Systems * Dynamical Systems on a Torus * The Phase Locked Loop * Models in Population Biology * Genetics
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications.
Appeals to researchers and graduate students who require tools to investigate stochastic systems.
This book covers the impact of noise on models that are widely used in science and engineering, and applies perturbed methods which assume noise changes on a faster time or space scale than the system being studied. The book is written in two parts. The first part carefully develops mathematical methods of studying random perturbations of dynamical systems. The second part presents non-random problems, reformulated to account for both external and system random noise, and analyzed using results from Part I. Researchers and graduate students in mathematics and engineering will find this book useful.