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Let (fn)n=1N be a stochastic process adapted to the filtration (F nn=0N). Denoting by (gn)n=1N the predictable projection of this process, i.e., gn=En−1(fn) we show that the inequality $$\left[ {E(\sum\limits_{n = 1}^N {|g_n |^q }...
We give a general group theoretic scheme for obtaining intertwining relations between Markov semi-groups. This is applied to the Heisenberg group and yields an intertwining relation between the Ornstein-Uhlenbeck and the Yule semi-groups.
The purpose of this paper is to compute the asymptotic probability that the solution of a stochastic differential equation with boundary conditions belongs to a small tube of radius ≠>0 centered around the solution of the deterministic equation without drift.
Résumé On majore le diamètre de l’ensemble des barycentres convexes d’une probabilité portée par un petit compact d’une variété avec connexion, par le moment d’ordre trois de la probabilité. Si le compact est un espace produit, on démontre que le projeté sur une composante de l’ensemble des barycentre convexes est l’ensemble des barycentres convexes de la loi marginale sur cette composante. ...
In this note a simple proof of the equivalence of the predictable representation property of a martingale with respect to a filtration associated with an orthogonal martingale measure and the extremality of the underlying probability measure P is given. The representation property enables us to characterize all measures which are locally absolutely continuous with respect to P. We apply this to superprocesses...
The chaotic representation property is given a meaning and established for a class of martingales X defined on some stochastic interval [0, T] and having only finitely many jumps before T−∈.
Results of Fristedt and Pruitt [6,7] on the lower functions of a subordinator are improved in the case when the Laplace exponent is slowly varying. This yields laws of the iterated logarithm for the local times of a class of Markov processes. In particular, this extends recent results of Marcus and Rosen [9] on certain Lévy processes close to a Cauchy process.
We establish an existence theorem for a class of SDE’s driven by Lévy processes on a manifold. As an application we consider an SDE driven by horizontal vector fields on the orthonormal frame bundle of a Riemannian manifold. The canonical projection of the solution of this equation on to the base is considered as a candidate for a “Lévy process on a Riemannian manifold”.
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