In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...

We study the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes driven by [alpha]-stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence 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...

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...

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 energy condition. As a consequence, the Fujisaki-Kallianpur-Kunita equation is also derived. Our results...

Purpose: Providing care that is patient-centered is an important objective in the modern healthcare industry. Despite this objective, hospital inpatient case managers and the services they provide are evaluated routinely without including patients' perspectives. Therefore, the purpose of this...