有记忆随机过程的Donsker函数

IF 0.5 Q4 MULTIDISCIPLINARY SCIENCES

Journal of Mathematical and Fundamental Sciences Pub Date : 2019-12-31 DOI:10.5614/j.math.fund.sci.2019.51.3.5

H. Suryawan

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引用次数: 2

摘要

在Hida微积分的框架内研究了一类具有记忆的随机过程。证明了过程的Donsker泛函是Hida分布。进一步推导了过程的概率密度函数和Donsker函数的混沌分解。作为应用，证明了Riemann-Liouville分数布朗运动作为白噪声广义函数在任意维上重整化局部时的存在性。

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Donsker’s Delta Functional of Stochastic Processes with Memory

A class of stochastic processes with memory within the framework of the Hida calculus was studied. It was proved that the Donsker delta functionals of the processes are Hida distributions. Furthermore, the probability density function of the processes and the chaos decomposition of the Donsker delta functional were derived. As an application, the existence of the renormalized local times in an arbitrary dimension of the Riemann-Liouville fractional Brownian motion as a white noise generalized function was proved.

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来源期刊

Journal of Mathematical and Fundamental Sciences MULTIDISCIPLINARY SCIENCES-

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health Sciences, Medical Sciences, Pharmacy), Mathematics, Physics, and Statistics. New submissions of mathematics articles starting in January 2020 are required to focus on applied mathematics with real relevance to the field of natural sciences. Authors are invited to submit articles that have not been published previously and are not under consideration elsewhere.