XV: 28, 388-398, LNM 850 (1981)
SPILIOTIS, Jean
Sur les travaux de Krylov en théorie de l'intégrale stochastique (Martingale theory)
The well-known work of Malliavin deals with the existence of smooth densities for solutions of stochastic differential equations with smooth coefficients satisfying a hypoellipticity condition. N.V.~Krylov's earlier work (among many papers see Izvestija Akad Nauk, 38, 1974, and Krylov's book Controlled Diffusion processes, Springer 1980) dealt with the existence of densities for several dimensional stochastic integrals with measurable bounded integrands, satisfying an ellipticity condition. It is a puzzling fact that nobody ever succeeded in unifying these results. Krylov's method depends on results of the Russian school on Monge-Ampère equations (see Pogorelov The Minkowski Multidimensional Problem, 1978). This exposition attempts, rather modestly, to explain in the seminar's language what it is all about, and in particular to show the place where a crucial lemma on convex functions is used
Keywords: Stochastic integrals, Existence of densities
Nature: Exposition
Retrieve article from Numdam

---