We are interested in a probabilistic approximation of the solution to scalar conservation laws with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation is based on a stochastic differential equation driven by an [alpha]-stable Lévy process and involving a...

Let be a d-dimensional array of independent standard Gaussian random variables. For a finite set define . Let A be the number of elements in A. We prove that the appropriately normalized maximum of , where A ranges over all discrete cubes or rectangles contained in {1,...,n}d, converges in law...

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the Threshold estimator is able to separate the integrated variance IV from the sum of...

In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we...

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a...

The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the driving vector field and the initial condition, and...

We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region, it is necessary to inspect a random number of neighborhood symbols which might...

Let W=(Wi)i[set membership, variant]N be an infinite dimensional Brownian motion and (Xt)t=0 a continuous adaptedn-dimensional process. Set [tau]R=inf{t:Xt-xt=Rt}, where xt,t=0 is a Rn-valued deterministic differentiable curve and Rt0,t=0 a time-dependent radius. We assume that, up to [tau]R,...

We extend the work of Delong and Imkeller (2010) [6] and [7] concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general Lp-spaces and provide sufficient conditions for the solution of a delay BSDE to exist...

We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which...