Thursday, Jan 26, 2017 - 3:30pm - Allen 14
An adaptive algorithm for solving stochastic boundary value problem
Davood Damircheli, Mathematics, Msstate
Title: An adaptive algorithm for solving stochastic boundary value problem
Abstract: Numerical methods to solve initial value problems in stochastic differential equations (SDE-IVPs) have been extensively researched in the last two decades. This is not the case for stochastic boundary value problems (SBVPs), because of complications both in theoretical as well as computational aspects. These equations appear naturally in a variety of fields such as smoothing, maximum a posteriori estimation of trajectories of diffusions, wave motion in random media, stochastic optimal control, valuation of boundary-linked assets, and in the study of reciprocal processes. They also arise from the semi-discretization of stochastic partial differential equations by the method of lines or Rothe's method. Taking into account the fact that the exact solution of these equations is rarely available in analytic form, trying to find efficient approximation schemes for the trajectories of the solution process or its moments, seems to be a natural candidate. I present an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems.We first analyze the strong order of convergence of the underlying multiple shooting method. We then proceed to describe the proposed strategy to adaptively choose the location of shooting points. We analyze the effect of method parameters on the performance of the overall scheme using a benchmark linear two-point stochastic boundary value problem.