S〓*(M)空间中的Bochner-Wick积分

doi:10.6040/j.issn.1671-9352.0.2019.655

摘要/Abstract

摘要： 设S ^*(M)为离散时间正规鞅M的广义泛函空间。主要在Bernoulli噪声分析框架下,引入和讨论关于S ^*(M)-值测度和S ^*(M)-值函数的积分运算。首先,定义S ^*(M)-值测度的概念,在此基础上利用Fock变换深入考察S ^*(M)-值测度的性质,获得这类测度在范数意义下可数可加的合适条件。其次,定义S ^*(M)-值函数关于S ^*(M)-值测度的Bochner-Wick积分,建立相应的控制收敛定理以及其它一些结果。

关键词: 离散时间正规鞅, Fock变换, Bochner-Wick积分, 向量测度

Abstract: Let S ^*(M)be a generalized functional space of discrete-time normal martingale M. This paper introduces and discusses the integral operation of S ^*(M)-valued measure and S ^*(M)-valued function in the framework of Bernoulli noise analysis. First of all, the concept of S ^*(M)-valued measure is defined. On this basis, this paper deeply investigates the properties of S ^*(M)-valued measure by Fock transform, and obtains the appropriate conditions for the countably additive of this kind of measure in the sense of norm. Next, Bochner-Wick integral for S ^*(M)-valued function with respect to S ^*(M)-valued measure is defined and the corresponding control convergence theorem is established.

Key words: discrete-time normal martingale, Fock transform, Bochner-Wick integral, vector measure

中图分类号:

O211.63

石佳,王才士,张丽霞,张银. S〓^*(M)空间中的Bochner-Wick积分[J]. 《山东大学学报(理学版)》, 2020, 55(6): 23-31.

SHI Jia, WANG Cai-shi, ZHANG Li-xia, ZHANG Yin. Bochner-Wick integral for S ^*(M)space[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 23-31.

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