一类线性随机Volterra积分方程的数值方法

Numerical Methods for a Class of Linear Stochastic Volterra Integral Equations

将Winner过程引入到经典的线性Volterra积分方程中,得到一类线性随机Volttera积分方程.研究这类随机积分方程解在平方可积空间中的存在性,证明了在均方意义下解的唯一性,并应用配置法构造了数值求解格式.数值实验验证了理论结果.

Winner process was introduced into the classical linear Voherra integral equations so as to get a class of linear stochastic Volterra integral equations. Firstly, we researched the existence of solution for this kind of stochastic integral equations in the square integral space, and then proved the uniqueness of solution in the sense of the mean square. We constructed the numerical scheme via collocation method, and numerical experiments confirmed our theoretical results.