4 research outputs found
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 , 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 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,