On distribution free Skorokhod-Malliavin calculus

TL;DR

This paper develops a distribution-free version of Skorokhod-Malliavin calculus based on uncorrelated random variables with known distributions, and explores its applications to stochastic PDEs.

Contribution

It introduces a novel distribution-free Skorokhod-Malliavin calculus framework without assumptions on distribution types, extending stochastic analysis tools.

Findings

Established a distribution-free calculus framework

Applied the calculus to stochastic PDEs

Demonstrated flexibility with unknown distribution structures

Abstract

The starting point of the current paper is a sequence of uncorrelated random variables. The distribution functions of these variables are assumed to be given but no assumptions on the types or the structure of these distributions are made. The above setting constitute the so called "distribution free" paradigm. Under these assumptions, a version of Skorokhod-Malliavin calculus is developed and applications to stochastic PDES are discussed.