复合白噪声驱动的输运方程

he Stochastic Transport Equation Driven by Combined\\White Noises

摘要: 本文在现有Gauss白噪声理论体系及L\'evy纯跳白噪声理论体系的基础上, 讨论了复合L\'evy白噪声分析的框架, 并将Wick乘积、Hermite变换等概念推广到复合L\'evy白噪声空间, 同时给出了与复合L\'evy白噪声空间对应的Hida分布空间的特征定理. 最后, 在本文的理论框架下, 详细讨论了由复合\, L\'evy白噪声驱动的随机输运方程在Hida分布空间中的解及其结构.

Abstract: In this paper, we develop a new framework of combined white noises basing on the existing Gaussian and pure jump L\'evy white noises. The Wick product, Hermite transform and the characterization theorem of Hida distribution space are generalized in this framework. Moreover, we solve the stochastic transport equation by the characterization theorem and discuss the solution in detail.