The large deviation principle is established for the Fleming-Viot process with neutral mutation when the process starts from a point on the boundary. Since the diffusion coefficient is degenerate on the boundary, the boundary behavior of the process is investigated…

A distribution (function) $F$ on $[0,1]$ with $F(t)$ less or equal $t$ for all $t$ is called subdiagonal. The extreme subdiagonal distributions are identified as those whose distribution functions are almost surely the identity, or equivalently for which $F \circ…

We give another proof of the following result from a joint paper with Bálint Tóth: A Brownian motion reflected on an independent time-reversed Brownian motion is a Brownian motion.

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

We study the optimal control problem for $\mathbb{R}^d$-valued absolutely continuous stochastic processes with given marginal distributions at every time. When $d=1$, we show the existence and the uniqueness of a minimizer which is a function of a time and an…

Using a transportation approach we prove that for every probability measures $P,Q_1,Q_2$ on $\Omega^N$ with $P$ a product measure there exist r.c.p.d. $\nu_j$ such that $\int \nu_j (\cdot|x) dP(x) = Q_j(\cdot)$ and $$ \int dP (x) \int \frac{dP}{dQ_1} (y)^\beta \frac{dP}{dQ_2}…

The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in $R^2$ and $R^3$. We assume that the flow is driven by an incompressible time-dependent random velocity field with Gaussian statistics. We also assume…

The law for the time $\tau_{a}$ spent by a standard Brownian excursion above a given level $a > 0$ is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark of an independent…

We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operator on the path space can yield in a very…

Consider the events $\{F_n \cap \bigcup_{k=1}^{n-1} F_k = \emptyset\}$, $n \in N$, where $(F_n)_{n=1}^\infty$ is an i.i.d. sequence of stationary random subsets of a compact group $G$. A plausible conjecture is that these events will not occur infinitely often with…