Uniform Approximation for Families of Stochastic Integrals

In view of the extensive use of stochastic integrals and stochastic differential equations in modeling of systems in engineering, and economic systems especially in mathematical finance and other applied problems, it is necessary to find whether there are good approximants to the stochastic integrals and the stochastic differential equations which can be used for simulation purposes. Some work in the area of approximations for the stochastic differential equations is in Rao et al. (1974) and Milshtein (1978). More recently, Kloeden and Platen (1992) gives a comprehensive discussion on the numerical solution of stochastic differential equations. Our aim in this paper is to study the uniform approximations for families of stochastic integrals both of the Ito type and Rubin-Fisk-Stratonovich type. The problem is of major interest especially when modelling is done by a stochastic differential equation involving unknown parameters and the uniform approximation of the stochastic integrals involved becomes important for simulation