Equivalent upper and lower bounds for the $L^1$ norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.

We consider ballistic diffusion limited aggregation on a finite strip $[0, L-1]$ times $\mathbb{Z}_+$ in $\mathbb{Z}^2$ for some $L$ in $\mathbb{Z}_+$. We provide numerical bounds on the growth in the height process.

We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The proof uses martingale identities and change of measure.

Let $A$ be an arc on the boundary of the unit disk $U$. We prove an asymptotic formula for the probability that there is a percolation cluster $K$ for critical site percolation on the triangular grid in $U$ which intersects…

We consider a continuous time random walk on the $d$-dimensional lattice $\mathbb{Z}^d$: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We investigate the implications  of heat kernel estimates on recurrence-transience  properties…

In 1971, Yamada and Watanabe showed that pathwise uniqueness holds for the SDE $dX= \sigma (X)dB$ when sigma takes values in the n-by-m matrices and satisfies $|\sigma (x)- \sigma (y)| < |x-y|\log(1/|x-y|)^{1/2}$. When $n=m=2$ and $\sigma$ is of the form…

Given a probability law $\pi$ on a set $S$ and a function $g : S \rightarrow R$, suppose one wants to estimate the mean $\bar{g} = \int g d\pi$. The Markov Chain Monte Carlo method consists of inventing and simulating…