NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD

Split-step Forward Milstein Method for Stochastic Differential Equations

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order γ = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability p...

Numerical Method for Backward Stochastic Differential Equations

We propose a method for numerical approximation of Backward Stochastic Differential Equations. Our method allows the final condition of the equation to be quite general and simple to implement. It relies on an approximation of Brownian Motion by simple random walk.

An analysis of stability of milstein method for stochastic differential equations with delay

-This paper deals with the adapted Milstein method for solving linear stochastic delay differential equations. It is proved that the numerical method is mean-square (MS) stable under suitable conditions. The obtained result shows that the method preserves the stability property of a class of linear constant-coefficient problems. This is also verified by several numerical examples. (~) 2006 Else...

An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler’s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable; however, no knowledge of advanced probability theory or stochastic processes is assumed. The article is built aro...

Simulation & Stochastic Differential Equations