In the last five years, the scientific computing community has taken great interest in the so-called stochastic Galerkin schemes (SGS). These schemes are typically used to address the following type of problem: Suppose that I have a deterministic differential equation model for which I can find an approximate solution using standard numerical discretization techniques. Now suppose that, in an a...

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described...

The purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws. In particular, we prove that, as in the case of stochastic differential systems affine in the control, one can compute stabilizing feedback laws provided the unforced stochastic differential system ...

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique give...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...