A sophisticated proof of the multiplication formula for multiple Wiener integrals
Ali S\"uleyman \"Ust\"unel
TL;DR
This paper presents a clear proof that the multiplication formula for multiple Wiener integrals, involving Wiener chaos decomposition, can be derived straightforwardly using Leibniz's rule.
Contribution
It provides a simple, rigorous proof of the multiplication formula for multiple Wiener integrals, clarifying its derivation using Leibniz's rule.
Findings
The multiplication formula for multiple Wiener integrals is validated.
The proof simplifies understanding of Wiener chaos decomposition.
The approach highlights the role of Leibniz's rule in stochastic calculus.
Abstract
We prove that the formula which gives the Wiener chaos decomposition of the multiplication of two multiple Wiener integrals with symmetric kernels is a straightforward application of the Leibniz' formula.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · advanced mathematical theories