Théorie spectrale d'un opérateur de transition sur un espace métrique compact
Théorie unifiée des capacités et des ensembles analytiques
There exists no ultimate solution to Skorokhod's problem
Thick points for the Cauchy process
Thick points for transient symmetric stable processes.
Thin points for brownian motion
Thinness and non-tangential limit associated to coupled PDE
In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ) and equations of type.
Three examples of brownian flows on
We show that the only flow solving the stochastic differential equation (SDE) on
Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior
Tightness results for laws of diffusion processes application to stochastic mechanics
Time dependent subordination and Markov processes with jumps
Time reversal for drifted fractional Brownian motion with Hurst index .
Time reversal of non-Markov point processes
Time-changes of self-similar Markov processes
Time-dependent barrier options and boundary crossing probabilities.
Time-dependent Schrödinger perturbations of transition densities
We construct the fundamental solution of for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We...
Time-homogeneous diffusions with a given marginal at a random time
We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab. 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof...
Time-homogeneous diffusions with a given marginal at a random time
We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab.20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give...
Time-space analysis of the cluster-formation in interacting diffusions.
Time-substitution based on fluctuating additive functionals (Wiener-Hopf factorization for infinitesimal generators)