We consider a random variable X satisfying almost-sure conditions involving G := DX; DL X where DX is X’s Malliavin derivative and L 1 is the pseudo-inverse of the generator of the OrnsteinUhlenbeck semigroup. A lower(resp. upper-) bound condition on G is proved to imply a Gaussian-type lower (resp. upper) bound on the tail P [X > z]. Bounds of other natures are also given. A key ingredient is ...

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanic...

where L is the left regular representation of G. From this it can be deduced that for any v in V and f in C c (G) the vector π(f) is smooth, and more precisely that if X lies in U(g) then π(X)π(f)v = π(LXf)v. This implies that V ∞ is dense in V , since if {fn} is a Dirac sequence on G then π(fn)v → v. The subspace of V ∞ spanned by the π(f)v with f in C c (G) is called the Gårding subspace of V...

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20

Consider stochastic functional differential equations depending on whole past histories in a finite time interval, which determine non-Markovian processes. Under the uniformly elliptic condition on the coefficients of the diffusion terms, the solution admits a smooth density with respect to the Lebesgue measure. In the present paper, we will study the large deviations for the family of the solu...

By using Malliavin calculus and multiple Wiener-Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces wit...

We derive Edgeworth-type expansions for Poisson stochastic integrals, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which are based on third cumulants instead of the L3 norm term found in the literature. The use of the third cumulant results into a convergence rate faster than the classical Berry-Es...

We study a parabolic SPDE driven by a white noise and a compensated Poisson measure. We rst de ne the solutions in a weak sense, and we prove the existence and the uniqueness of a weak solution. Then we use the Malliavin calculus in order to show that under some non-degeneracy assumptions, the law of the weak solution admits a density with respect to the Lebesgue measure. To this aim, we introd...

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter H > 1/2. Our results rely on recent tools of Young integration for convolutional integrals combined with stochastic analysis methods for the study of laws of random variables defined on a Wiener sp...

We consider a class of multidimensional inhomogeneous diffusions whose drift coefficient depends on unknown parameter. Under some appropriate assumptions, we prove the local asymptotic mixed normality property for parameter from high-frequency observations when length observation window tends to infinity. To obtain result, use Malliavin calculus techniques and change measures. Our approach is a...