This article was motivated by a question of Kesten. Kesten asked for which random walks periodic sceneries can be reconstructed. Among others, he asked the question for random walks which at each step can move by one or two units to the right. Previously, Howard [C.D. Howard,...

We study a Hamilton-Jacobi-Bellman equation related to the optimal control of a stochastic semilinear equation on a Hilbert space X. We show the existence and uniqueness of solutions to the HJB equation and prove the existence and uniqueness of feedback controls for the associated control...

In this paper we obtain the smoothness of the diffusion coefficient matrix for the generalized exclusion process.

We consider Sinai's random walk in a random environment. We prove that for an interval of time [1,n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi-totality of this amount of time. Moreover the local time at the point of localization normalized by n...

The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of 'disorder' when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is...

One of two simple hypotheses for the unknown arrival rate and jump distribution of a compound Poisson process is correct. We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision. We find a...

We study the existence and smoothness of densities of laws of solutions of a canonical stochastic differential equation (SDE) driven by a Lévy process through the Malliavin calculus on the Wiener-Poisson space. Our assumption needed for the equation is very simple, since we are considering the...

In the Hammersley harness processes the -valued height at each site is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in . With this representation we...

We give asymptotic bounds for sample paths of discrete time infinitely divisible processes and prove the optimality of such bounds.

The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case where the value function is assumed to be continuous in time and once differentiable in the space variable...