On SPDE and backward filtering equations for SDE systems (direct approach)

TL;DR

This paper introduces a direct approach to linear backward filtering equations for stochastic differential equation (SDE) systems, combining insights from previous works to improve understanding and solution methods for SPDEs in filtering problems.

Contribution

It presents a novel direct method for solving linear backward filtering equations in SDE systems, building on and correcting earlier research from 1995.

Findings

Provides a corrected and unified approach to backward filtering equations

Enhances solution techniques for linear SPDEs in SDE systems

Bridges previous theoretical work with new direct solution methods

Abstract

A direct approach to linear backward filtering equations for SDE systems is proposed. This preprint is a corrected version of the paper 1995 in the LMS Lecture Notes combined with another paper by the author on the direct approach to linear SPDEs for SDEs.