La méthode d'approximation de Gauss-Galerkin en filtrage non linéaire
Laplace asymptotics for generalized K.P.P. equation
Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle...
Laplace asymptotics for generalized K.P.P. equation
Laplace transform identities for diffusions, with applications to rebates and barrier options
We start with a general time-homogeneous scalar diffusion whose state space is an interval I ⊆ ℝ. If it is started at x ∈ I, then we consider the problem of imposing upper and/or lower boundary conditions at two points a,b ∈ I, where a < x < b. Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms...
Le rôle de l'énergie libre pour des systèmes régis par l'équation de Fökker-Planck
Likely path to extinction in simple branching models with large initial population.