Dynamical Systems Perturbed by Noise: the Langevin Equation

Abstract

In this monograph we analyse the dynamics of finite-dimensional nonlinear systems that are perturbed by noise. The type of systems we deal with arises in different fields of applications, such as in stochastic mechanics and in the dynamics of biological populations. Depending on the application, the noise may have quite different origins. Outside fluctuations affecting a physical system can be incorporated in the modelling in the form of a stochastic input. The system may have intrinsic stochastics, for example in the birth-death process in population dynamics. Another possibility is to account for components neglected in the model by adding noise terms. As a result of the noise the value of the state vector X(t) of a system is uncertain.