We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the…

We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and d-dimensional simplex. Central limit theorems with convergence…

We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give…

We study an infinite white $\alpha$-stable systems with unbounded interactions, and prove the existence of a solution by Galerkin approximation and an exponential mixing property by an $\alpha$-stable version of gradient bounds.

We study lattice trees, lattice animals, and percolation on non-Euclidean lattices that correspond to regular tessellations of two- and three-dimensional hyperbolic space. We prove that critical exponents of these models take on their mean field values. Our methods are mainly…

This paper has four interrelated themes: (1) express Laplace and Mellin transforms of sums of positive random variables in terms of the Mellin transform of the summands; (2) show the equivalence of the two Barnes' lemmas with known properties of…

We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $\mathbb{Z}$ starting from an arbitrary initial profile. We generalize earlier works by Seppalainen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas…

We study the dynamics of a certain discrete model of interacting interlaced particles that comes from the so called shuffling algorithm for sampling a random tiling of an Aztec diamond. It turns out that the transition probabilities have a particularly…

A necessary and sufficient condition for the tail of an infinitely divisible distribution on the real line to be estimated by the tail of its Lévy measure is found. The lower limit and the upper limit of the ratio of…