Energy and the law of the interated logarithm.
Ensembles régénératifs, d'après Hoffmann-Jørgensen
Erneuerungsprozesse.
Estimates for the distribution of the first exit time of α-stable processes
The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
Estimates for the Poisson kernel on higher rank NA groups
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
Estimates on the solution of an elliptic equation related to Brownian motion with drift (II).
In this paper we continue the study of the Dirichlet problem for an elliptic equation on a domain in R3 which was begun in [5]. For R > 0 let ΩR be the ball of radius R centered at the origin with boundary ∂Ω R. The Dirichlet problem we are concerned with is the following:(-Δ - b(x).∇) u(x) = f(x), x ∈ Ω R,with zero boundary conditionsu(x) = 0, x ∈ ∂Ω R.
Euclidean quantum mechanics : analytical approach
Exchangeable fragmentation-coalescence processes and their equilibrium measures.
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...
Extended piecewise Markov processes in continuous time
Extended piecewise Markov processes in discrete time
Extending the Wong-Zakai theorem to reversible Markov processes
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...