Patrick Cattiaux

Quasi-stationary distributions and diffusion models in population dynamics

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to

Competitive or weak cooperative stochastic Lotka–Volterra systems conditioned on non-extinction

- \infty

Concentration for independent random variables with heavy tails

at the origin, and the diffusion to have an entrance boundary at

Poincaré inequalities and hitting times

+\infty

Large deviations and Nelson processes

. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth--death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with probability

Large deviations and variational theorems for marginal problems

1

Existence of a quasi-markov nash equilibrium for non-zero sum markov stopping games

. An important example is the logistic Feller diffusion. We give sufficient conditions on the drift near

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model

0

Time reversal of diffusion processes with a boundary condition

and near

A Biased Competition Theory of Cytotoxic T Lymphocyte Interaction with Tumor Nodules

+ \infty