A high order time discretization of the solution of the non-linear filtering problem
arXiv:1711.08012
Abstract
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of these functionals of arbitrary order. The result generalizes the classical work of Picard, who introduced first order discretizations to the filtering functionals. For a given time interval partition, we construct discretization schemes with convergence rates that are proportional with the -power of the mesh of the partition for arbitrary . The result paves the way for constructing high order numerical approximation for the solution of the filtering problem.
50 pages