Stochastic differential equations

In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ_c, where α measures the size of the fluctuations and τ_c their autocorrelation time. This result is the underlying reason for the existence of “renormalized transport coefficients”. In chapter III the same treatment is adapted to nonlinear equations. In chapter IV an alternative treatment is described, applicable only in a special case, but not confined to small ατ_c.The emphasis is on physical usefulness rather than mathematical rigor. Throughout the text applications are given at the points where they appeared to serve best as illustrations of the method. The list of references is not complete, but hopefully representative of the literature.