On the stochastic Benjamin–Ono equation

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

On the Stochastic Kuramoto-Sivashinsky Equation

In this article we study the solution of the Kuramoto–Sivashinsky equation on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time and depends continuously on the initial data.

On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold

We prove the existence and the uniqueness of a solution to the stochastic NSLEs on a two-dimensional compact riemannian manifold. Thus we generalize (and improve) a recent work by Burq et all [11] and a series of papers by de Bouard and Debussche, see e.g. [16, 17] who have examined similar questions in the case of the at euclidean space. We prove the existence and the uniqueness of a local max...

On Numerical Approximation of Stochastic Burgers’ Equation

A Remark on Tsirelson's Stochastic Differential Equation

| Tsirelson's stochastic di erential equation is called \celebrated and mysterious" by Rogers and Williams bd16ce. This note aims at making it a little more celebrated and a little less mysterious. Using a deterministic time-change, we translate the study of Tsirelson's equation into the study of \eternal" Brownian motion on the circle. This allows us to show that the ltration generated by any ...