We correct an error in Electronic Communications in Probability, Vol 15 (2010), paper 10

We prove the existence of a solution for the Kolmogorov equation associated with a reflection problem for 2-D stochastic Navier-Stokes equations with periodic spatial conditions and the corresponding stream flow in a closed ball of a Sobolev space of the…

We consider the white-noise driven stochastic heat equation on $[0,1]$ with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the $L^1([0,1])$-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some…

We consider the interlacement Poisson point process on the space of doubly-infinite $\mathbb{Z}^d$-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is…

We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan…

We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination…

We analyze the tail behavior of the maximum $N$ of $\{W(t)-t^2:t\ge0\}$, where $W$ is standard Brownian motion on $[0,\infty)$, and give an asymptotic expansion for ${\mathbb P}\{N\ge x\}$, as $x\to\infty$. This extends a first order result on the tail behavior,…

We prove a law of large numbers for the right boundary in the model of internal DLA generated by cookie random walks in dimension one. The proof is based on stochastic recursions techniques.

It is shown that a stochastic process obtained by taking random sums of dilations and translations of a given function converges to Gaussian white noise if a dilation parameter grows to infinity and that it converges to Gaussian colored noise…

Construction methods for Feller processes which require bounded coefficients are extended to the case of unbounded coefficients.