ABSTRACT
Stochastic differential equations provide flexible models for stochastic modeling in continuous time and space, and also powerful probabilistic tools for the numerical solution of partial differential equations via the expectation of functionals of the corresponding processes. The Euler scheme for stochastic differential equations is a natural extension of the Euler scheme for an ordinary differential equation: it consists of locally freezing the coefficients on small time intervals. This is a natural extension of the scheme for ordinary differential equations. The version for stochastic differential equations was first proposed by Maruyama and sometimes is called the Euler-Maruyama scheme.
