On Stochastic Change Of Parameters For Stochastic Integrals With Parameters

A stochastic integral is the integral of a stochastic process with respect to another stochastic process.For a stochastic integral with the integrand containing a parameter,under what conditions can the operation of integration and the operation of replacing the parameter with a raindom variable commutate?Such a question is meaningful both in theory and in application.In this thesis,we aim at looking for an answer to the above question.By tak-ing a deep examination of stochastic integrals with integrands containing parameters,we obtain several sets of sufficient conditions for the above-mentioned operations to commutate,respectively in the three cases listed below:· The integrator is Brown motion,while the integrand is a continuous adapted pro-cess;· The integrator is Brown motion,while the integrand is a square integrable adapted process;· The integrator M is a continuous L2-martingale,while the integrand is an M-square integrable predictable process.Examples are given to show the usefulness and efficiency of our conditions,and some other results are also proven of stochastic integrals containing parameters.