Etude de l'endroit et de l'instant de premier passage de certains processus de diffusion (French text).

摘要

In this study, two functionals were considered for a number of diffusion processes in order to determine the time and position of first passage across the boundary of the domain in which the given processes evolve.; This study was done from the differential stochastic equation of the considered process in order to first obtain a partial differential equation by using the method of differential equations, and then an ordinary differential equation using the method of similarity solutions.; In the first chapter, we gave an introduction to the basic necessary notions to understand this work. In the second chapter, we studied the time of first passage for a number of diffusion processes; more specifically we determined the moment generating function of the time of first passage for these processes. In the third chapter, we studied the position of first passage for certain diffusion processes.; Finally, in the fourth chapter, we were interested in the place of first passage of the integrated Bessel process and of the generalized Bessel process.