The chemostat is classically represented, at high population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives ri...

We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection diffusion reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type inter-particle interactions. Furthermore, we consider a new, asymmetric, single exclusion process, studied elsew...

In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

Although the concept of symmetry is widely used in many fields, it almost not discussed finance. This appears to be relevant relation, for example, mathematical models that can predict stock prices contribute decision-making process. work considers price European options with a new class non-constant delay model. The stochastic pantograph differential equation (SPDE) variable provided order ove...

Heart failure is one of the significant public health burdens in world. According to WHO, 2 million people suer heart worldwide. In this study, we propose a bivariate stochastic model for disease progression and recovery process, which helps understand underlying mechanisms process suggests strategies improve performance system. Sensitivity analysis carried out behavior.