In this paper, Hunt’s hypothesis (H) and Getoor’s conjecture for Lévy processes are revisited. Let X be a Lévy process on Rn with Lévy–Khintchine exponent (a,A,μ). First, we show that if A is non-degenerate then X satisfies (H). Second, under the assumption that μ(Rn∖ARn)∞, we...

Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dirichlet form setting. Then, we study the uniqueness of solutions of the...

Herein, we consider direct Markov chain approximations to the Duncan-Mortensen-Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are...