Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all...

Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

We revisit the R-positivity of nearest neighbor matrices on and the Gibbs measures on the set of nearest neighbor trajectories on whose Hamiltonians award either visits to sites or visits to edges. We give conditions that guarantee the R-positivity or equivalently the existence of the infinite...

We study a polymer model on hierarchical lattices very close to the one introduced and studied in Derrida and Griffith (1989) [19] and Cook and Derrida (1989) [16]. For this model, we prove the existence of free energy and derive the necessary and sufficient condition for which very strong...

The mean excess plot is a tool widely used in the study of risk, insurance and extreme values. One use is in validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot.

The study of discrete-time stochastic processes on the half-line with mean drift at x given by [mu]1(x)--0 as x--[infinity] is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case where [mu]1(x) is of order x-[beta] for some [beta][set membership,...

We first establish a general version of the Birkhoff Ergodic Theorem for quasi-integrable extended real-valued random variables without assuming ergodicity. The key argument involves the Poincaré Recurrence Theorem. Our extension of the Birkhoff Ergodic Theorem is also shown to hold for...

An urn contains balls of d=2 colors. At each time n=1, a ball is drawn and then replaced together with a random number of balls of the same color. Let diag (An,1,...,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available...

This paper studies a system of backward stochastic differential equations with oblique reflections (RBSDEs for short), motivated by the switching problem under Knightian uncertainty and recursive utilities. The main feature of our system is that its components are interconnected through both the...

We prove the existence of an invariant measure [mu] for the transition semigroup Pt associated with the fast diffusion porous media equation in a bounded domain , perturbed by a Gaussian noise. The Kolmogorov infinitesimal generator N of Pt in is characterized as the closure of a second-order...