Some Recent Results in Nonlinear Filtering Theory with Finitely Additive White Noise

摘要

Nonlinear filtering theory has been developed over the last few decades, largely, as an application of stochastic calculus. The theory (which will be referred to below as the conventional or stochastic calculus theory) has led to many important new advances in the subject and, indeed, given rise to problems of interest to stochastic calculus itself. When it comes to statistical applications, however, the approach based on stochastic calculus has many shortcomings which originate from the use of the Wiener process as a model for noise. This point has been recognized by many writers and has led to attempts to create a pathwise or robust version of the theory this article presents a very brief outline of an alternative approach developed recently in collaboration with R.L. Karandikar. In this theory, the Wiener process is replaced by finitely additive (f.a.) Gaussian which noise in the filtering model in which we also assume the independence of signal and noise.