Kernel representation formula from complex to real Wiener-Ito integrals and vice versa
Probability
2022-07-21 v1
Abstract
We clearly characterize the relation between real and complex Wiener-Ito integrals. Given a complex multiple Wiener-Ito integral, we get explicit expressions for two kernels of its real and imaginary parts. Conversely, consider a two-dimensional real Wiener-Ito integral, we obtain the representation formula by a finite sum of complex Wiener-Ito integrals. The main tools are a recursion technique and Malliavin derivative operators. We build a bridge between real and complex Wiener-Ito integrals.
Cite
@article{arxiv.2207.09637,
title = {Kernel representation formula from complex to real Wiener-Ito integrals and vice versa},
author = {Huiping Chen and Yong Chen and Yong Liu},
journal= {arXiv preprint arXiv:2207.09637},
year = {2022}
}