Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space (0,1/2]×L2(T,m), (T,m) a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional Brownian motion. This field encompasses a large class of...

In this paper we discuss a credit risk model with a pure jump Lévy process for the asset value and an unobservable random barrier. The default time is the first time when the asset value falls below the barrier. Using the indistinguishability of the intensity process and the likelihood process,...

Let W be a Wiener process. For r0 and T0 let IW(T,r)2 denote the minimal value of the energy ∫0Th′(t)2dt taken among all absolutely continuous functions h(⋅) defined on [0,T], starting at zero and satisfying W(t)−r≤h(t)≤W(t)+r,0≤t≤T. The function minimizing energy is a taut...

We describe all random sets that satisfy the radial conformal restriction property, therefore providing the analogue in the radial case of results of Lawler, Schramm and Werner in the chordal case.

By using Bismut’s approach to the Malliavin calculus with jumps, we establish a derivative formula of Bismut–Elworthy–Li’s type for SDEs driven by multiplicative Lévy noises, whose Lévy measure satisfies some order conditions. In particular, α-stable-like noises are allowed. Moreover,...

The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the Λ-coalescent. In particular we formulate the infinite population “Λ-lookdown model with selection”. When the...

Motivated by the recent results of Nualart and Xu (2013) concerning limits laws for occupation times of one dimensional symmetric stable processes, this paper proves a decomposition for functionals of one dimensional symmetric Lévy processes under certain conditions on the characteristic...

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of “naturally occurring” strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise...

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on Zd, d≥2. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of...

We study a class of self-similar jump type SDEs driven by Hölder continuous drift and noise coefficients. Using the Lamperti transformation for positive self-similar Markov processes we obtain a necessary and sufficient condition for almost sure extinction in finite time. We then show that in...