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This book covers stochastic differential equations involving two well-separated timescales (in other words, singularly perturbed, or slow-fast systems with noise). It's major goal is to provide constructive methods to characterise the typical paths of these equations, in order to obtain physically relevant information.  The first part of the book is devoted to a systematic study of these singularly perturbed stochastic differential equations, starting with a one-dimensional study, then proceeding to multi-dimensional systems. Special attention is paid to the effect of noise on dynamic bifurcations near which transition phenomena are most likely to be observed.  The rest of the book is devoted to case studies and applications. A whole chapter is devoted to stochastic resonance, and other applications including models of solid-state physcis and climatology.
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