Let Z be a stochastic process of the form Z(t)=Z(0)exp([mu]t+X(t)-<X>t/2) where Z(0)0, [mu] are constants, and X is a continuous local martingale having a deterministic quadratic variation <X> such that <X>t--[infinity] as t--[infinity]. We show that the mantissa (base b) of Z(t) (denoted by M(b)(Z(t))...</x></x></x>

This paper considers the following generalized almost sure local extinction for the d-dimensional (1+[beta])-super-Brownian motion X starting from Lebesgue measure on . For any t=0 write for a closed ball in with center at 0 and radius g(t), where g is a nonnegative, nondecreasing and right...

We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a Lévy process. The main interest of this work is to compare the rates induced by "exact" and "approximate"...

Let be a random field indexed by an Abelian compact group G, and suppose that has the form , where T is Gaussian and stationary. The aim of this paper is to establish high-frequency central limit theorems for the Fourier coefficients associated with . The proofs of our main results involve...

We investigate the high resolution quantization and entropy coding problem for solutions of stochastic differential equations under supremum norm distortion. Tight asymptotic formulas are found under mild regularity assumptions. The main technical tool is a decoupling method which allows us to...

Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected instantaneously on the left and right sides with constant...

We consider a heat conduction model for solids. Nearest neighbour atoms interact as coupled oscillators exchanging velocities in such a way that the total energy is conserved. The system is considered under periodic boundary conditions. We will show that the system has a hydrodynamic limit given...

This paper proposes two related approximation schemes, based on a discrete grid on a finite time interval [0,T], and having a finite number of states, for a pure jump Lévy process Lt. The sequences of discrete processes converge to the original process, as the time interval becomes finer and...

A scalar valued random field is called operator-scaling if for some dxd matrix E with positive real parts of the eigenvalues and some H0 we have where denotes equality of all finite-dimensional marginal distributions. We present a moving average and a harmonizable representation of stable...

The aim of this paper is to use non-asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to stochastic mechanics and calibration problems for diffusion...