The goal of this article is to provide a largely self-contained introduction to the modelling of
controlled quantum systems under continuous observation, and to the design of feedback …

Many aspects of phenomena critical to our lives can not be measured directly. Fortunately
models of these phenomena, together with more limited observations frequently allow us to …

We extend Echeverria's criterion for invariant measures for a Markov process characterized
via martingale problems to the case where the state space of the Markov process is a …

This paper concerns the control of diffusions under partial observations. Part I studies the
control of the signal process dX_t=b(t,X_t,U_t)dt+σ(t,X_t,U_t)dB_t, when the observation is …

Onwards from the mid-twentieth century, the stochastic filtering problem has caught the
attention of thousands of mathematicians, engineers, statisticians, and computer scientists …

Stochastic filtering is defined as the estimation of a partially observed dynamical system.
Approximating the solution of the filtering problem with Gaussian mixtures has been a very …

In this paper we consider classical and quantum spin systems on discrete lattices and in
Euclidean spaces, modeled by infinite dimensional stochastic diffusions in Hilbert spaces …

We survey the development and role of stochastic differential equations in filtering theory.
The basic stochastic differential equation of Fujisaki, Kallianpur, and Kunita, which solves …

Let X be a Markov process taking values in a complete, separable metric space E and
characterized via a martingale problem for an operator A. We develop a criterion for …

In this paper, we give a direct derivation of the Duncan–Mortensen–Zakai filtering equation,
without assuming right continuity of the signal, nor its filtration, and without the usual finite …