2022/07/20 by Huiping Chen, Yong Chen, Chen, Huiping +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2207.09637
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.