Approximation of Multiple Stochastic Integrals and Its Application to Stochastic Differential Equations Original Research Article

As multiple stochastic integrals are not very easy to simulate, we would like to treat them as solutions of systems of stochastic differential equations and solve them successively and recursively approximated by the stochastic Taylor expansion as a Chen series in terms of a Philip Hall basis or Lyndon basis. We can save sufficient values of multiple stochastic integrals with independent sample paths in a look-up table for future use. The table can be used to implement high order schemes to solve stochastic differential equations numerically. A numerical example will be shown to illustrate the efficiency.