By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order H ∈ ( 12 , 1)). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satis es a non-central limit theorem and its limit is (in the L(Ω) sense) still ...

Let V be a multiplication operator, whose negative part, V-(V-< 0) obeys-A + (1 + c)V->-c for some c, c > 0. Let W = Vx where x is the characteristic function of the exterior of a ball. Our main result asserts that the scattering for-A + V is complete if and only if that for-A + W is complete. Our technical estimates exploit Wiener integrals and the Feynman-Kac formula. We also make an applicat...

Abstract This paper aims to construct adaptedness and stochastic integration on Poisson space in the abstract setting of Hilbert spaces with minimal hypothesis, in particular without use of any notion of time or ordering on index sets. In this framework, several types of stochastic integrals are considered on simple processes and extended to larger domains. The results obtained generalize the e...

This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of partition lattices and Möbius functions. Gaussian and Poisson measures are treated in great detail. We also present several combinatorial interpretations of ...

This paper aims to construct adaptedness and stochastic integration on Poisson space in the abstract setting of Hilbert spaces with minimal hypothesis, in particular without use of any notion of time or ordering on index sets. In this framework, several types of stochastic integrals are considered on simple processes and extended to larger domains. The results obtained generalize the existing c...

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...

By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-Itô integrals, we define a 2D-stochastic current over the Brownian sheet. This concept comes from geometric measure theory. We also study the regularity of the stochastic current with respect to the randomness variable in the Watanabe spaces and with respect to the spatial variable in the determini...