Malliavin calculus and decoupling inequalities in Banach spaces
نویسندگان
چکیده
منابع مشابه
Malliavin Calculus and Decoupling Inequalities in Banach Spaces
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided L-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-I...
متن کاملConcentration inequalities via Malliavin calculus with applications
We use the Malliavin calculus to prove a new abstract concentration inequality result for zero mean, Malliavin differentiable random variables which admit densities. We demonstrate the applicability of the result by deriving two new concrete concentration inequalities, one relating to an integral functional of a fractional Brownian motion process, and the other relating to the centered maximum ...
متن کاملUniversal Malliavin Calculus in Fock and Lévy-Itô Spaces
We review and extend Lindsay’s work on abstract gradient and divergence operators in Fock space over a general complex Hilbert space. Precise expressions for the domains are given, the L2-equivalence of norms is proved and an abstract version of the Itô-Skorohod isometry is established. We then outline a new proof of Itô’s chaos expansion of complex Lévy-Itô space in terms of multiple Wiener-Lé...
متن کاملDensity estimates and concentration inequalities with Malliavin calculus
We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and use a new formula for the density ρ of a random variable Z which is measurable and di erentiable with respect to a given isonormal Gaussian process. Among other results, we apply our techniques to bound the density o...
متن کاملDensity formula and concentration inequalities with Malliavin calculus
We show how to use the Malliavin calculus to obtain a new exact formula for the density ρ of the law of any random variable Z which is measurable and di erentiable with respect to a given isonormal Gaussian process. The main advantage of this formula is that it does not refer to the divergence operator (dual of the Malliavin derivative). In particular, density lower bounds can be obtained in so...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.08.041