Nonlinear Filtering and Smoothing of Diffusions

Abstract

Filtering theory is concerned with the extraction of information from noisy measurements of a signal. For example, in radio communications the signal may be speech, music, or data, which are converted by a microphone or a computer into a variable voltage x(t) or a vector of variable voltages x(t). The signal is often assumed to be a stationary random process and is often characterized by its power spectral density function. Linear filtering theory is by now a classical subject that has been thoroughly discussed in the literature. Nonlinear filtering, however, is still a subject of intensive research.