Article ID Journal Published Year Pages File Type
1140180 Mathematics and Computers in Simulation 2009 10 Pages PDF
Abstract

In the construction of numerical methods for solving stochastic differential equations it becomes necessary to calculate the expectation of products of multiple stochastic integrals. Well-known recursive relationships between these multiple integrals make it possible to express any product of them as a linear combination of integrals of the same type. This article describes how, exploiting the symbolic character of Mathematica, main recursive properties and rules of ItĂ´ and Stratonovich multiple integrals can be implemented. From here, a routine that calculates the expectation of any polynomial in multiple stochastic integrals is obtained. In addition, some new relations between integrals, found with the aid of the program, are shown and proved.

Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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