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Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted...

Stochastic differential equations whose solutions are diffusion (or other random) processes have been the subject of lively mathematical research since the pioneering work of Gihman, Ito and others in the early fifties. As it gradually became clear that a great number of real phenomena in control theory, physics, biology, economics and other areas could be modelled by differential equations with stochastic perturbation terms, this research became somewhat feverish, with the results that a) the number of theroretical papers alone now numbers several hundred and b) workers interested in the...