一类高阶热方程解的随机计算

Stochastic Calculus for Solutions of a Class of High Order Parabolic Equation

本文给出一类“马氏过程”A-过程的随机积分的定义,证明随机积分的存在性及A过程函数的IT(?)公式。应用IT(?)公式给出一类高阶热方程解的随机表达式。

In this paper, stochastic integrals for A-processes x(t); t≥0,related to the equations (?)u(t,x) = (-1)n+1 (?)2nu(t,x),n≥2, are introduced. ITO formula of a function of A-process is proven.The stochastic solution of the following initial value problem is given in the form u(t,x) = Ex{(?)(X(t))} + Ex((?)0'f(t - r,X(r))dr} by using the ITO formula.