Multiple stochastic integrals with Mathematica

  • Authors:

  • A. Tocino

  • Affiliations:

  • Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced, 1, 37008 Salamanca, Spain

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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 Ito 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.