This work describes a Galerkin type method for stochastic partial differential equations of Zakai type driven by an infinite dimensional càdlàg square integrable martingale. Error estimates in the semidiscrete case, where discretization is only done in space, are derived in L and almost sure senses. Simulations confirm the theoretical results.

This 1)aper addresses the stochastic modeling for managing asset liability process. We start with developing a jump-diffusion process for evaluating of the liabilities of the insurance company in general. We then tbrnmlate the ALM process into a stochastic control problem. With this approach, we present a Bel|man-Dreyfus Fundamental type formula for ALM process in terms of the solution of a sys...

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called “method of the moving frame” allows us to reduce the proof to the Yamada-Watanabe Theorem for stochastic differential equations in infinite dimensions.

Motivated by ongoing work in the theory of stochastic partial differential equations we develop direct methods to infer that the Galerkin approximations of certain nonlinear partial differential equations are Cauchy (and therefore convergent). We develop such a result for the Navier–Stokes equations in space dimensions two and three, and for the primitive equations in space dimension two. The a...

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...