d维N参数分数布朗运动局部时的混沌分解

Chaos Decomposition of Local Time for d-Dimensional Fractional Brownian Motion with N-Parameter

  • 摘要: 本文在经典白噪声分析框架下, 研究分数布朗运动局部时的存在性与混沌分解. 我们用白噪声分析方法证明维1个参数的分数布朗运动的局部时是一个Hida广义泛函. 在一定的条件下, 该局部时在中存在. 进一步, 利用埃尔米特多项式给出了该局部时的维纳--伊藤清混沌分解. 最后, 类似地获得了维个参数情形的结果. 我们推广了文献Bakun(2000)中所获得的布朗运动情形下的一些结果.

     

    Abstract: In this paper, the existence and chaos decomposition of local time of fractional Brownian motion are studied within the canonical framework of white noise analysis. We prove that the local time of -dimensional fractional Brownian motion with 1-parameter is a Hida distribution through white noise approach. Under some conditions, it exists in . Moreover, the Wiener-Ito chaos decomposition of it is also given in terms of Hermite polynomials. Finally, similar results of -dimensional fractional Brownian motion with -parameter are also obtained. We popularize some results in Bakun (2000) for the case of Brownian motion.

     

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