NON-DEGENERACY OF WIENER FUNCTIONALS ARISING FROM ROUGH DIFFERENTIAL EQUATIONS

被引：39

作者：

Cass, Thomas ^{[1
]}

Friz, Peter ^{[1
]}

Victoir, Nicolas ^{[1
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Stat, Cambridge CB3 0WB, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 06期

关键词：

Malliavin Calculus; rough paths analysis; FRACTIONAL BROWNIAN-MOTION; DRIVEN;

D O I：

10.1090/S0002-9947-09-04677-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of the solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss the existence of a density for solutions to stochastic differential equations driven by a general class of non-degenerate Gaussian processes, including processes with sample path regularity worse than Brownian motion.

引用

页码：3359 / 3371

页数：13

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