由两个独立的Lévy过程的差分解多个Wiener积分空间

Q2 Mathematics

Communications on Stochastic Analysis Pub Date : 2018-10-01 DOI:10.31390/COSA.12.2.05

Atsushi Ishikawa

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引用次数: 0

摘要

本文将随机过程作用于多个Wiener积分的lsamvy Laplacian看作是两个独立lsamvy过程的差分，并给出了lsamvy Laplacian的特征函数的一个充分必要条件。此外，通过上述过程，我们给出了l杂讯概率空间上l2空间的分解，即由多个Wiener积分组成的特征空间在l杂讯概率空间上的分解。通过这种分解，我们得到了与数算子生成的半群相关的lsamvy拉普拉斯半群的表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Decomposition of a Space of Multiple Wiener Integrals by the Difference of Two Independent Lévy Processes in Terms of the Lévy Laplacian

In this paper, we consider the Lévy Laplacian acting on multiple Wiener integrals by the stochastic process given as a difference of two independent Lévy processes, and give a necessary and sufficient condition for eigenfunctions of the Lévy Laplacian. Moreover we give a decomposition of the L2-space on Lévy noise probability space by eigenspaces consisting of multiple Wiener integrals by the above process in terms of the Lévy Laplacian. By this decomposition, we obtain an expression of the semigroup generated by the Lévy Laplacian related to the semigroup generated by the number operator.

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来源期刊

Communications on Stochastic Analysis Mathematics-Statistics and Probability

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： The journal Communications on Stochastic Analysis (COSA) is published in four issues annually (March, June, September, December). It aims to present original research papers of high quality in stochastic analysis (both theory and applications) and emphasizes the global development of the scientific community. The journal welcomes articles of interdisciplinary nature. Expository articles of current interest will occasionally be published. COSAis indexed in Mathematical Reviews (MathSciNet), Zentralblatt für Mathematik, and SCOPUS