We show that for certain bounded cylinder functions of the form F(x) = μ̂((h1,x)∼, . . . ,(hn,x)∼), x ∈ B, where μ̂ :Rn → C is the Fourier-transform of the complexvalued Borel measure μ on (Rn), the Borel σ -algebra of Rn with ‖μ‖ < ∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iq Iaw(F ;z)= limz→−iq(z/2π) ∫ Rn f( →u)exp{−(z/2)| →u|2}d →u, do not alwa...

This paper considers the asymptotic behaviour of volumes excursion sets subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals such and obtain their limiting distribution using Hermite expansion integrand. We general non-stationary fields, including stationary anisotropic special cases. The variables in our limit theorems have form mult...

We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-Itô integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nuala...

This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevan...

Abstract. In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions of a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The approximation is given in terms of discrete-jumping filtrations which allow us...

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotrop...

We show that the coherent state matrix elements of the quantum mechanical propagator for all quadratic Hamiltonians may be represented as the limit of path integrals with respect to appropriately modified Wiener measures as the associated diffusion constant tends to infinity. In this letter we state some results concerning path integrals with genuine mathematically welldefined measures to defin...

In 2005, Nualart and Peccati [12] showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-Itô integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. [8] extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the fre...

In this paper we present two methods for computing filtered estimates for moments of integrals and stochastic integrals of continuous-time nonlinear systems. The first method utilizes recursive stochastic partial differential equations. The second method utilizes conditional moment generating functions. An application of these methods leads to the discovery of new classes of finitedimensional f...