We construct the law of Lévy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then… (More)

Using Lamperti’s relationship between Lévy processes and positive self-similar Markov processes (pssMp), we study the weak convergence of the law IPx of a pssMp starting at x > 0, in the Skorohod… (More)

We prove that when a sequence of Lévy processes X(n) or a normed sequence of random walks S(n) converges a.s. on the Skorokhod space toward a Lévy process X, the sequence L(n) of local times at the… (More)

We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the… (More)

Quantitative plant disease resistance is believed to be more durable than qualitative resistance, since it exerts less selective pressure on the pathogens. However, the process of progressive… (More)

A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a… (More)

In this paper we derive some distributional properties of Levy processes and bridges from their cyclic exchangeability property. We first describe the 03C3-field which is invariant under the cyclic… (More)

A Lévy forest of size s > 0 is a Poisson point process in the set of Lévy trees which is defined on the time interval [0, s]. The total mass of this forest is defined by the sum of the masses of all… (More)

Data obtained from ISSR amplification may readily be extracted but only allows us to know, for each gene, if a specific allele is present or not. From this partial information we provide a… (More)