Discovery of rare event testing for stochastic simulations of diffusion processes

Abstract

Stochastic modeling of diffusion processes in various spatial domains and with boundary conditions is widely applicable especially in combination with non-linear kinetics of chemical reactions. However, the comparison with exact solution is possible in simple cases e.g. linear diffusion models. The novel testing method introduced in this article enables to study the behavior of linear stochastic diffusion models with possible low particle concentration in target sub-domains. The proposed method is demonstrated on various diffusion models with the known Green function. The novel method is recommended whenever the chi(2) goodness-of-fit test fails or the localization of critical domains is required.