Absolute continuity for some one-dimensional processes

被引:49
作者
Fournier, Nicolas [1 ]
Printems, Jacques [1 ]
机构
[1] Univ Paris Est, Lab Anal & Math Appl, CNRS, Fac Sci & Technol,UMR 8050, F-94010 Creteil, France
关键词
absolute continuity; Holder coefficients; Levy processes; random coefficients; stochastic differential equations; stochastic partial differential equations; PARTIAL-DIFFERENTIAL EQUATIONS; DRIVEN PARABOLIC SPDES; MALLIAVIN CALCULUS; EXISTENCE; DENSITY; DRIFT;
D O I
10.3150/09-BEJ215
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler approximation of the underlying process. We obtain some absolute continuity results for stochastic differential equations with Holder continuous coefficients. Furthermore, we allow such coefficients to be random and to depend on the whole path of the solution. We also show how it can be extended to some stochastic partial differential equations and to some Levy-driven stochastic differential equations. In the cases under study, the Malliavin calculus cannot be used, because the solution in generally not Malliavin differentiable.
引用
收藏
页码:343 / 360
页数:18
相关论文
共 26 条