Density Formula and Concentration Inequalities with Malliavin Calculus
نویسندگان
چکیده
منابع مشابه
Density 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...
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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...
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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 ...
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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...
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We derive and analyze Monte Carlo estimators of price sensitivities (“Greeks”) for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is t...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2009
ISSN: 1083-6489
DOI: 10.1214/ejp.v14-707