In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.

We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normaliz...

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...

We extend the definition of Walsh’s martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green’s function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even when the integrand is a distribution, the value of our stochastic integral process is a real-valued martinga...

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...

We associate with a stochastic cocycle Θ = (φ,Φ), on Y = Ω×H, a stochastic variational integral equation and we characterize the exponential instability in mean square of stochastic equations in therms of solvability of the associated equation. Thus we obtain a generalization of stochastic case for results obtained by O. Perron [8], in deterministic case. 2000Mathematics Subject Classification:...