Characterization of Hida Measures in white noise analysis

Wiener空间上的重整化群：谱理论与普适性

Renormalization Group on Wiener Space: Spectral Theory and Universality

本文在Wiener空间上建立严格重整化群形式体系，通过白噪声分析实现谱理论，揭示Donsker不变原理中修正层级的新普适性，并恢复量子场论中的标准分类。

Stochastic Quantization of Laser Propagation Models

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts the problem reduces to stochastic Schrodinger equation with space-time white noise of Gaussian, Poisson and Levy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by stochastic nonlinear Schrodinger equation in the focusing case with space-time white noise. A treatment of stochastic transport equation, the Korteweg-de…

Regularity of Gaussian white noise on the d-dimensional torus

In this paper we prove that a Gaussian white noise on the $d$-dimensional torus has paths in the Besov spaces $B^{-d/2}_{p,\infty}(\T^d)$ with $p\in [1, \infty)$. This result is shown to be optimal in several ways. We also show that Gaussian white noise on the $d$-dimensional torus has paths in a the Fourier-Besov space $\hat{b}^{-d/p}_{p,\infty}(\T^d)$. This is shown to be optimal as well.

On the structure of non-commutative white noises

We consider the concepts of continuous Bernoulli systems and non-commutative white noises. We address the question of isomorphism of continuous Bernoulli systems and show that for large classes of quantum L{é}vy processes one can make quite precise statements about the time behaviour of their moments.

A White Noise Approach to Phase Space Feynman Path Integrals

The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrödinger equation are obtained and the canonical commutation relations are satisfied. The later can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.