Convergence of Implicit Discretization Schemes for Linear Differential Equations with Application to Filtering.

摘要

The motivation for the present work arises from a well-known problem in nonlinear filtering. If one wants to solve it recursively 'online' on a digital computer, the best one can do is to provide well-behaved discretization algorithms in both space and time. It is useful to design algorithms that discretize but still retain the representation, merely changing the process involved. This could be obtained by replacing the diffusion by a continuous- time finite-state Markov chain with generator A(sub h), which of course is of the finite difference type (the simplest example is provided by H. J. Kushner). But it continues to hold if time is implicitly discretized and the stochastic Trotter product formula is used.