We prove short-time existence for parabolic equations with Lévy noise of the form where is nonnegative Lévy noise of index is the power of the Laplacian, , and is a continuous nonnegative function. is a bounded open domain in . A sufficient condition for short time existence is While we cannot...

We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold...

We consider an optimal control problem for an Itô diffusion and a related stopping problem. Their value functions satisfy (d/dx)V=u and an optimal control defines an optimal stopping time. Conversely, we construct an optimal control from optimal stopping times, find a representation of V as an...

We prove existence, uniqueness and comparison theorems for a class of semilinear stochastic partial differential equations driven by space-time white noise. The class of equations we investigate contains as special cases the stochastic Burgers equation and the reaction-diffusion equations...

We study a generalised version of the logistic map of the unit interval in which the point is taken to . Here, is a parameter of the map, which has received attention only when and . We obtain the invariant density when , and derive properties of invariant distributions in all other cases. These...

A model of symmetric random evolution in a plane with , directions controlled by a homogeneous Poisson process is studied. A governing high-order hyperbolic equation is obtained. Its parabolic approximation is also given.

We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

This paper deals with the fractional step method in the analysis of stochastic partial differential equations (SPDEs) and their generalizations. Three types of problems are investigated. The first one is the study of invariant sets for the solution of the stochastic equations. The second one is...

Let denote the expected number of crossings of a level , in a fixed time interval [0,1], by a large class of real valued symmetric stationary harmonizable infinitely divisible processes which includes stationary harmonizable stable processes. Equivalent upper and lower bounds are given for and a...

Using the generalized Campbell theorem, a functional (distributional) version of Little's law is obtained for general FIFO systems with non-anticipating arrivals. Our approach generalizes existing results and, in particular, points out the intimate relation between the Palm-Khintchine equations...