arXiv subjects

Jia-an Yan

Publications and source records attributed to Jia-an Yan.

3 recordsLinked to original sources

arXiv2009

Wick Calculus For Nonlinear Gaussian Functionals

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. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the $S$-transform which is also described without the introduction of generalized random variables.

math.PR↗

arXiv2008

General Matrix-Valued Inhomogeneous Linear Stochastic Differential Equations and Applications

The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential equations. As an application, some $\R^n$ vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating pathwise study of the solutions.

math.DS↗

arXiv2002

Generalized Functions in Infinite Dimensional Analysis

We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.

math.FA↗