Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations.
Dynamics and density evolution in piecewise deterministic growth processes
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.
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...
First eigenvalue of one-dimensional diffusion processes.
First hitting time and place, monopoles and multipoles for pseudo-processes driven by the equation .
Fonctionnelles multiplicatives opératrices
Fractional Brownian motion and the Markov property.
Fragmentation of ordered partitions and intervals.
From convergence of operator semigroups to gene expression, and back again
The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by means of a...