We provide here some sharp Schauder estimates for degenerate PDEs of Kolmogorov type when the coefficients lie in some suitable anisotropic Hölder spaces and the first order term is non-linear and unbounded. We proceed through a perturbative approach based on forward parametrix expansions.Due to the low regularizing properties of the degenerate variables, for the procedure to work, we heavily exploit duality results between appropriate Besov spaces.Our method can be seen as constructive and provides, even in the non-degenerate case, an alternative approach to Schauder estimates.

No abstract

No abstract

Abstract. The goal of this paper is to present a series of recent contributions on some various problems of numerical probability. Beginning with the Richardson-Romberg Multilevel Monte-Carlo method which, among other fields of applications, is a very efficient method for the approximation of diffusion processes, we focus on some adaptive multilevel splitting algorithms for rare event simulation. Then, the third part is devoted to the simulation of McKean-Vlasov forward and decoupled forwardbackward stochastic differential equations by some cubature algorithms. Finally, we tackle the problem of the weak error estimation in total variation norm for a general Markov semi-group.