Euler-Maruyama method for non-Wiener processes

Abstract

Descriptions of complex physical or biological systems often include stochastic contributions, and these are commonly simulated using Wiener processes. In many cases however, non-Gaussian fluctuations may originate from non-Wiener processes which remain less explored. The Euler-Maruyama method of discretising stochastic differential equations to non-Wiener processes is generalised. Non-Gaussian noise generated from a subset of Lévy processes can be used simply and often with more physical justification, for both additive and multiplicative noise. An example of this is provided that gives superior physical results compared to using geometric Brownian motion. Finally the results of the additive noise are shown to be equivalent to a derived master equation via the Kramers-Moyal expansion.