Factorising brownian motion at two boundaries ; an example
Filtrations browniennes et balayage
Formules de changement de variables
Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes
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...
From Tanaka's formula to Ito's formula : distributions, tensor products and local times
Fubini's theorem for double Wiener integrals and the variance of the brownian path
Function decompositions related to the Luzin N-property.
Generalised transforms, quasi-diffusions, and Désiré André's equation
Géométrie de la courbe brownienne plane
Homogeneous random measures and strongly supermedian kernels of a Markov process.
How does a reflected one-dimensional diffusion bounce back?
Intermittency and ageing for the symbiotic branching model
For the symbiotic branching model introduced in [Stochastic Process. Appl.114 (2004) 127–160], it is shown that ageing and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with brownian potential. Some refinements to more general (also infinite range) kernels of recent ageing results of [Ann. Inst. H. Poincaré...
Interprétation d'un calcul de H. Tanaka en théorie générale des processus
Intersection Local Times and Tanaka Formulas
Invariance principles for Brownian intersection local time and polymer measures.
Itô formula and local time for the fractional Brownian sheet.
Joint continuity of renormalized intersection local times
is not a semimartingale
inequalities for functionals of brownian motion