For stochastic differential equations with jumps, we prove that W1H transportation inequalities hold for their invariant probability measures and for their process-level laws on the right-continuous path space w.r.t. the L1-metric and uniform metric, under dissipative conditions, via Malliavin...

We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This specific self-interaction leads to nonlinear stochastic...

For a strictly stationary sequence of random vectors in we study convergence of partial sum processes to a Lévy stable process in the Skorohod space with J1-topology. We identify necessary and sufficient conditions for such convergence and provide sufficient conditions when the stationary...

This paper proposes two main contributions concerning the Föllmer-Schweizer decomposition (called hereafter the FS-decomposition). First we completely elaborate the relationship between this decomposition and the Galtchouk-Kunita-Watanabe decomposition under the minimal martingale measure. The...

We consider a discretionary stopping problem that arises in the context of pricing a class of perpetual American-type call options, which include the perpetual American, Russian and lookback-American call options as special cases. We solve this genuinely two-dimensional optimal stopping problem...

In a seminal work, Bertil Matérn introduced several types of processes for modeling repulsive point processes. In this paper an algorithm is presented for the perfect simulation of the Matérn III process within a bounded window in , fully accounting for edge effects. A simple upper bound on...

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time/large scale behaviour of such a process under diffusive rescaling. Our main result is that it converges...

The Curie-Weiss Potts model is a mean field version of the well-known Potts model. In this model, the critical line [beta]=[beta]c(h) is explicitly known and corresponds to a first-order transition when q2. In the present paper we describe the fluctuations of the density vector in the whole...

The paper deals with curvilinear boundary crossing probabilities for time-homogeneous diffusion processes. First we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and the first passage time density. Namely, let [tau] be the first crossing time...

Let (Xt,t=0) be a random walk on . Let be the local time at the state x and the q-fold self-intersection local time (SILT). In [5] Castell proves a large deviations principle for the SILT of the simple random walk in the critical case q(d-2)=d. In the supercritical case q(d-2)d, Chen and...