Avoiding-probabilities for Brownian snakes and super-Browian motion.
Un arbre aléatoire infini associé à l'excursion brownienne
Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients
We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for which the assumptions...
Changing the branching mechanism of a continuous state branching process using immigration
We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type,...
Pruning Galton–Watson trees and tree-valued Markov processes
We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process by pruning Galton–Watson trees and an analogous process by pruning a critical or subcritical Galton–Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process run until its ascension time has a representation in terms of . A similar result was obtained by Aldous and...
Page 1