Philippe Carmona

Beta-gamma random variables and intertwining relations between certain Markov processes

In this paper, we study particular examples of the intertwining relation Qt? = ?Pt between two Markov semi-groups (Pt, t = 0) defined respectively on (E,e) and (F,F), via the Markov kernel ?: (E,e) ? (F,F).

Sur les fonctionnelles exponentielles de certains processus de lévy

In this article we generalize the work of the third author concerning the law of , where ξ is a Brownian motion with drift and T an independent exponential time, to the case where ξ belongs to a certain class of Levy processes. Our method hinges on a bijection, introduced by Lamperti, between exponentials of Levy processes and semi-stable Markov processes

Approximation of Some Gaussian Processes

We study a class of processes which have a moving average representation with respect to a fixed driving martingale, and can be represented as a mixture of semi-martingale processes. When the driving martingale is Gaussian we obtain a numerically efficient approximation scheme and a central limit theorem (a typical process in this class is fractional Brownian motion).

The spread of a catalytic branching random walk

We consider a random walk on

Interacting partially directed self avoiding walk: scaling limits

\Z

Interacting partially directed self avoiding walk. From phase transition to the geometry of the collapsed phase

that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position

The discrete-time parabolic Anderson model with heavy-tailed potential

M_n

Stochastic integration with respect to fractional brownian motion

. Then we determine all possible limiting law for the sequence

On the partition function of a directed polymer in a Gaussian random environment

M_n -\alpha n

Universality In Sherrington-Kirkpatrick's Spin Glass Model

where