Second Moment Random Process Stochastic Integral And Boundary Value Problems

In this paper, we mainly study the following three problems.In the second chapter, using the criterion of loeve, we prove the random function , which is the symmetric function of the analytical random functionΦ(ω,z) defined in interior domain S+ of the unit circle, is also an analytic function. So we can get a mean square function defined in the whole area. Then we convert random hilbert boundary value problem into random riemann problem by this method, and get the solution of random hilbert problem finally.In the third chapter, we study several properties of random integral of random process with second order moment. By using these properties and boundary value theory of analytic functions, we obtain some properties of random singular integral with cauchy kernel. Moreover, we prove the plemelj formula corresponding to random singular integral with cauchy kernel of random process with second order moment in [1] by another method.In the fourth chapter, the existence theorem on random singular integral with hilbert kernel and the corresponding plemelj formula are considered. Our results extend the corresponding ones made in [1] by Wang Chuanrong.