Abstract:

Winner process was introduced into the classical linear Volterra 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.

Key words: stochastic Volterra integral equations, contraction mapping theorem, collocation method