Related papers: Wick Calculus For Nonlinear Gaussian Functionals
The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered…
Let $S=\mathbb{T}^d$ be a torus and $\mu$ the probability distribution of a L\'evy white noise field $x:S\rightarrow\mathbb{R}$. Using projective limit measures we address the problem of making sense of $\mathrm{e}^{-T(x)}$, where $T(x) =…
A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
We discuss different representations of the White noise spaces $(E)_{\beta}$, $0 \leq \beta < 1$ by introducing generalized Wick tensors. As an application we state a generalization of the Mehler formula for the Ornstein-Uhlenbeck…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…
The Kadanoff-Wilson-Fisher approach to renormalization is based upon studying the renormalization transform, which may be described as an action of the monoid $\mathbb{R}^{\times}_{\geq 1}$ on a suitable space of interactions. It is…
We consider Gaussian random waves on hyperbolic spaces and establish variance asymptotics and central limit theorems for a large class of their integral functionals, both in the high-frequency and large domain limits. Our strategy of proof…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
In this paper we establish a framework for normal approximation for white noise functionals by Stein's method and Hida calculus. Our work is inspired by that of Nourdin and Peccati (Probab. Theory Relat. Fields 145, 75-118, 2009), who…
We consider the defocusing nonlinear Schr\"odinger equations on the two-dimensional compact Riemannian manifold without boundary or a bounded domain in $\R^2$. Our aim is to give a pedagogic and self-contained presentation on the Wick…
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given,…
We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observed, whose dimension equals the number of additive…
Given a Gaussian stationary increment processes with spectral density, we show that a Wick-Ito integral with respect to this process can be naturally obtained using Hida's white noise space theory. We use the Bochner-Minlos theorem to…
Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron--Martin), differential calculus (Malliavin), support description (Stroock--Varadhan),…
We study the Cauchy problem for the nonlinear wave equations (NLW) with random data and/or stochastic forcing on a two-dimensional compact Riemannian manifold without boundary. (i) We first study the defocusing stochastic damped NLW driven…
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…
We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for…
In quantum field theory, the in and out states can be related to the full Hamiltonian by the $i\epsilon$ prescription. A Wick rotation can further bring the correlation functions to Euclidean spacetime where the integrals are better…
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…