Reverse Khas'minskii condition

The aim of this paper is to present and discuss some equivalent characterizations of p-parabolicity in terms of existence of special exhaustion functions. In particular, Khas'minskii in [K] proved that if there exists a 2-superharmonic function k defined outside a compact set such that $\lim_{x\to \infty} k(x)=\infty$, then R is 2-parabolic, and Sario and Nakai in [SN] were able to improve this result by showing that R is 2-parabolic if and only if there exists an Evans potential, i.e. a 2-harmonic function $E:R\setminus K \to \R^+$ with \lim_{x\to \infty} \E(x)=\infty. In this paper, we will prove a reverse Khas'minskii condition valid for any p>1 and discuss the existence of Evans potentials in the nonlinear case.Comment: final version of the article available at http://www.springer.co

Dispersion and collapse in stochastic velocity fields on a cylinder

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space

Recursive parameter estimation: asymptotic expansion

Recursive estimation, Estimating equations, Stochastic approximation, Exponential families of Markov processes,