A uniqueness result is proven for the infinitesimal generator associated with the 2D Euler flow with periodic boundary conditions in the space L2([mu]) with respect to the natural Gibbs measure [mu] given by the enstrophy. This result remains true for the generator of the stochastic process...

We study the three-dimensional stochastic Navier-Stokes equations with additive white noise, in the context of spatially homogeneous solutions in , i.e. solutions with a law invariant under space translations. We prove the existence of such a solution, with the additional property of being...

For certain Gaussian processes X(t) with trend -ct[beta] and variance V2(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t)-ct[beta]=u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in...

Max-stable processes arise in the limit of component-wise maxima of independent processes, under appropriate centering and normalization. In this paper, we establish necessary and sufficient conditions for the ergodicity and mixing of stationary max-stable processes. We do so in terms of their...

Some sufficient conditions for the recurrence, the positive recurrence and the exponential ergodicity of one-dimensional Lévy type operators are presented. The conditions are classified according to different conditions on the ranges and integrability of the Lévy measure, based on the drift...

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised...

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate [lambda]. When a new pathogen is born, it has the same type as its parent with probability 1-r. With probability r, a mutation occurs, and the new pathogen has a different type from...

Extending the recent work of Philippe et al. [A. Philippe, D. Surgailis, M.-C. Viano, Invariance principle for a class of non stationary processes with long memory, C. R. Acad. Sci. Paris, Ser. 1. 342 (2006) 269-274; A. Philippe, D. Surgailis, M.-C. Viano, Time varying fractionally integrated...

Through a regularization procedure, a few schemes for approximation of the local time of a large class of continuous semimartingales and reversible diffusions are given. The convergence holds in the ucp sense. In the case of standard Brownian motion, we have been able to bound the rate of...

In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance [alpha]-stable Lévy motion. We show that the solution is regularly varying with index [alpha]. An important step in the proof is the study of...