Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa
Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa
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DOI：
10.1016/j.spa.2023.104241
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发表时间：
2024
期刊：
影响因子：
--
通讯作者：
刘勇
中科院分区：
文献类型：
--
作者：
陈惠萍;陈勇;刘勇
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.
