An L¹Approximation for conditional expectations

Abstract

This paper presents two results: first, a theoretical result about convergence of conditional expectations; and second, a filtering approximation. A pair of time-homogeneous diffusions (X Y) on a probability space is approximated in distribution by a pair of birth-death Markov chains on , in such a way that conditional expectations calculated from the approximating system also converge (in distribution) to those of the limiting system. Then we move to a filtering context, and approximate conditional expectations of the form (for bounded and continuous) by an measurable estimate which converges in L ¹(P) uniformly on [O,T].

Keywords:

• Conditional expectations for diffusions
• Radon-Nikodym derivative
• absolutely continuous change of measure
• AMS Subject Classifications: 60, 94