. Stochastic Differential Equations

Application of DJ method to Ito stochastic differential equations

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

APPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES

We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...