Approximation of Stochastic Nonlinear Equations of Schrodinger Type by the Splitting Method

作者：Grecksch Wilfried^*; Lisei Hannelore

来源：Stochastic Analysis and Applications, 2013, 31(2): 314-335.

DOI：10.1080/07362994.2013.759745

• Infinite dimensional Wiener process
• Nonlinear stochastic Schrodinger equations
• Splitting method

In this article, we construct a splitting method for nonlinear stochastic equations of Schrodinger type. We approximate the solution of our problem by the sequence of solutions of two types of equations: one without stochastic integral term, but containing the Laplace operator and the other one containing only the stochastic integral term. The two types of equations are connected to each other by their initial values. We prove that the solutions of these equations both converge strongly to the solution of the Schrodinger type equation.

• 出版日期2013-3-1