A characterization of Markov solutions for stochastic differential equations with jumps
A counterexample for the Markov property of local time for diffusions on graphs
A deterministic displacement theorem for Poisson processes.
A diffusion model for two parallel queues with processor sharing: Transient behavior and asymptotics.
A direct proof of the Ray-Knight theorem
A Donsker theorem to simulate one-dimensional processes with measurable coefficients
In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.
A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors.
A modification of Sudakov's lemma and efficient sequential plans for the Ornstein-Uhlenbeck process
A new inequality for superdiffusions and its applications to nonlinear differential equations.
A note on a.s. finiteness of perpetual integral functionals of diffusions.
A note on estimation in controlled diffusion processes
A note on occupation times of stationary processes.
A note on one-dimensional stochastic equations
We consider the stochastic equation where is a one-dimensional Brownian motion, is the initial value, and is a time-dependent diffusion coefficient. While the existence of solutions is well-studied for only measurable diffusion coefficients , beyond the homogeneous case there is no general result on the uniqueness in law of the solution. The purpose of the present note is to give conditions on ensuring the existence as well as the uniqueness in law of the solution.
A note on the enumeration of diffusion walks in the first octant by their number of contacts with the diagonal.
A PDE approach to certain large deviation problems for systems of parabolic equations
A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities
A probabilistic approach to the boundedness of singular integral operators
A representation formula for large deviations rate functionals of invariant measures on the one dimensional torus
We consider a generic diffusion on the 1D torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had been characterized by M. I. Freidlin and A. D. Wentzell as solution of a rather complex optimization problem. We discuss this last problem in full generality and show that it leads to our formula. We express the rate functional by means of a geometric transformation...
A reversibility problem for Fleming-Viot processes.
A simple proof of the Poincaré inequality for a large class of probability measures.