William Oçafrain (Nancy)
This problem deals with a particle in movement in a set D in R^2. It moves according to two random parameters: the angle of the direction, which is chosen uniformly between 0 and 2?, and the time which the particle takes to move in straight line, which follows an exponential distribution of parameter 1. The particle continues to move until it touches the edge of D : the particle is then killed by the edge of D. The aim of the study is to analyze the behavior of the particle conditioned to be alive. More precisely we want to know, given a time t, the probability of presence of the particle at the time t, and the quasi-stationary distribution of the system, that’s to say the limit of the probability when the time tends to the infinity.
