Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa

Huiping Chen, Yong Chen and Yong Liu

Stochastic Processes and their Applications, 2024, vol. 167, issue C

Abstract: We characterize the relation between the real and complex Wiener–Itô integrals. Given a complex multiple Wiener–Itô integral, we get explicit expressions for the kernels of its real and imaginary parts. Conversely, considering a two-dimensional real Wiener–Itô integral, we obtain the representation formula by a finite sum of complex Wiener–Itô integrals. The main tools are a recursion technique and Malliavin derivative operators. As an application to stochastic processes, we investigate the regularity of the stationary solution of the stochastic heat equation with dispersion.

Keywords: Complex Wiener–Itô integral; Two-dimensional real Wiener–Itô integral; Generalized Stroock’s formula; Stochastic heat equation with dispersion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104241

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