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- Nicolas PRIVAULT, Xiao WEI
- 2005

We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation and to the construction of a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard… (More)

- Nicolas Privault
- 1999

We introduce on the Fock space ?(L 2 (I R +)) two operators r and r expressing the in-nitesimal perturbations of random variables by time changes in the Wiener and Poisson probabilistic interpretations of ?(L 2 (I R +)). These operators have close connections with stochastic integration, regularity of laws, chaotic expansions and complement the annihilation… (More)

- Nicolas Privault
- 1996

We show that two multiple stochastic integrals I n (f n), I m (g m) with respect to the solution (M t) t2I R + of a deterministic structure equation are independent if and only if two contractions of f n and g m , denoted as f n 0 1 g m , f n 1 1 g m , vanish almost everywhere.

- Virginie Debelley, Nicolas Privault, Michel Crépeau

We present a Malliavin calculus approach to sensitivity analysis of European options in a jump-diffusion model. The lack of differentiability due to the presence of a jump component is tackled using partial differentials with respect to the (absolutely continuous) Gaussian part. The method appears to be particularly efficient to compute sensitivities with… (More)

- NICOLAS PRIVAULT
- 2009

We prove a moment identity on the Wiener space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral on the Wiener space. As simple consequences of this identity we obtain sufficient conditions for the Gaussianity of the law of the Skorohod integral and a recurrence relation for the moments of second order Wiener integrals. We also… (More)

We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] ⋄ W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative,⋄ is the Wick product and W (t) is 1-dimensional Gaussian white… (More)

We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative, is the Wick product and W (t) is 1-dimensional Gaussian white noise.… (More)

—Ambient RF (Radio Frequency) energy harvesting techniques have recently been proposed as a potential solution to provide proactive energy replenishment for wireless devices. This paper aims to analyze the performance of a battery-free wireless sensor powered by ambient RF energy harvesting using a stochastic-geometry approach. Specifically, we consider a… (More)

- Nicolas Privault
- 2001

Torsion free connections and a notion of curvature are introduced on the in-nite dimensional nonlinear connguration space ? of a Riemannian manifold M under a Poisson measure. This allows to state identities of Weitzenbb ock type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a… (More)

The gradient and divergence operators of stochastic analysis on Rieman-nian manifolds are expressed using the gradient and divergence of the at Brownian motion. By this method we obtain the almost-sure version of several useful identities that are usually stated under expectations. The manifold-valued Brownian motion and random point measures on manifolds… (More)