For a Poisson high-density system of independent motions in we consider the corresponding density process as the limit of fluctuations or, equivalently, the limit of the "total charge" if each particle is equipped with a random charge. We prove that under fairly general assumptions on the...

In this paper, some explicit solutions are given for stochastic differential equations in a Hilbert space with a multiplicative fractional Gaussian noise. This noise is the formal derivative of a fractional Brownian motion with the Hurst parameter in the interval (1/2,1). These solutions can be...

When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample n individuals from a population and trace their ancestral lines backwards in time, many lineages may...

We study the 1/H-variation of the indefinite integral with respect to fractional Brownian motion for , where this integral is defined as the divergence integral in the framework of the Malliavin calculus. An application to the integral representation of Bessel processes with respect to...

We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitly the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of dimension 1+1 and 1+2. We also discuss the case of...

In this paper we study a class of backward stochastic differential equations with reflections (BSDER, for short). Three types of discretization procedures are introduced in the spirit of the so-called Bermuda Options in finance, so as to first establish a Feynman-Kac type formula for the...

A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of k given consecutive digits (significant digits) appears in the b-adic expansion of X approaches b-k as the block moves to the right, for all integers b1 and k[greater-or-equal,...

We study a formulation of regular variation for multivariate stochastic processes on the unit interval with sample paths that are almost surely right-continuous with left limits and we provide necessary and sufficient conditions for such stochastic processes to be regularly varying. A version of...

We consider a buffered queueing system that is fed by a Gaussian source and drained at a constant rate. The fluid offered to the system in a time interval (0,t] is given by a separable continuous Gaussian process Y with stationary increments. The variance function of Y is assumed to be regularly...

We establish Chung-Mogulskii type functional laws of the iterated logarithm for medium and large increments of the uniform empirical and quantile processes. This gives the ultimate sup-norm distance between various sets of properly normalized empirical increment processes and a fixed function of...