In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure is carried by the set {t:Xt=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on...

We consider a jumping Markov process . We study the absolute continuity of the law of for t0. We first consider, as Bichteler and Jacod [K. Bichteler, J. Jacod, Calcul de Malliavin pour les diffusions avec sauts, existence d'une densité dans le cas unidimensionel, in: Séminaire de...

We study Stratonovich s.d.e. driven by semimartingales in the tangent bundle over a differentiable manifold M. In ordinary differential geometry, a connection on M is needed to define the covariant derivative of a C1 curve in ; by the transfer principle, Elworthy and Norris have defined a...

We consider a filtering problem when the state process is a reflected Brownian motion Xt and the observation process is its local time [Lambda]s, for s=t. For this model we derive an approximation scheme based on a suitable interpolation of the observation process [Lambda]t. The convergence of...

Let us consider a pair signal-observation ((xn,yn),n=0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional distribution of yn only depends on the corresponding...

We consider a numerical scheme approximation for a diffusion on a Riemannian manifold using a normal chart approach and prove that it coincides with the modified Milstein scheme introduced in [A.B. Cruzeiro, P. Malliavin, A. Thalmaier, Geometrization of Monte-Carlo numerical analysis of an...

We study the exit problem of solutions of the stochastic differential equation from bounded or unbounded intervals which contain the unique asymptotically stable critical point of the deterministic dynamical system . The process L is composed of a standard Brownian motion and a symmetric...

We give a functional limit theorem for the fluctuations of the rescaled occupation time process of a critical branching particle system in with symmetric [alpha]-stable motion and [alpha]d2[alpha], which leads to a long-range dependence process involving sub-fractional Brownian motion. We also...

In this paper, the investigation into stochastic calculus related with the KdV equation, which was initiated by S. Kotani [Construction of KdV-flow on generalized reflectionless potentials, preprint, November 2003] and made in succession by N. Ikeda and the author [Quadratic Wiener functionals,...

In this paper we introduce and study a regularizing one-to-one mapping from the class of one-dimensional Lévy measures into itself. This mapping appeared implicitly in our previous paper [O.E. Barndorff-Nielsen, S. Thorbjørnsen, A connection between free and classical infinite divisibility,...