分数布朗运动的指数泛函
The Exponential Functional of Fractional Brownian Motion
DOI: 10.12677/PM.2020.1010111, PDF,   
作者: 胡鑫宇, 闫理坦：东华大学理学院，上海；郭 睿：东华大学信息学院，上海
关键词: 分数布朗运动；随机游动；特征函数；Fractional Brownian Motion； Random Walk； Characteristic Function
摘要: 本文旨在研究分数布朗运动指数泛函∫0teσBsH-μsds,σ∈R,μ>0，Hurst指数H∈(1/2,1)的离散化与分布问题。
Abstract: In this note, we will investigate the discrete approximations and the characteristic function of the exponential functional of fractional Brownian motion ∫0teσBsH-μsds,σ∈R,μ>0 with Hurst index H∈(1/2,1).
文章引用：胡鑫宇, 郭睿, 闫理坦. 分数布朗运动的指数泛函[J]. 理论数学, 2020, 10(10): 953-961. https://doi.org/10.12677/PM.2020.1010111

参考文献

[1] Dufresne, D. (1990) The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding. Scandi-navian Actuarial Journal, 1990, 39-79. [Google Scholar] [CrossRef] 
[2] Dufresne, D. (2010) G Distributions and the Beta-Gamma Algebra. Electronic Journal of Probability, 15, 2163-2199. [Google Scholar] [CrossRef] 
[3] Dufresne, D. (2001) The Integral of Geometric Brownian Motion. Ad-vances in Applied Probability, 33, 223-241. [Google Scholar] [CrossRef] 
[4] Dufresne, D. (1989) Weak Convergence of Random Growth Process with Applications to Insurance. Insurance: Mathematics and Economics, 8, 187-201. [Google Scholar] [CrossRef] 
[5] Yor, M. (1992) On Some Exponential Functional of Brown-ian-Motion. Advances in Applied Probability, 24, 509-531. [Google Scholar] [CrossRef] 
[6] Szabados, T. and Szekely, B. (2010) An Exponential Functional of Random Walks. Journal of Applied Probability, 40, 413-426. [Google Scholar] [CrossRef] 
[7] Szabados, T. and Székely, B. (2004) Moments of an Exponential Functional of Random Walks and Permutations with Given Descent Sets. Periodica Mathematica Hungarica, 49, 131-139. [Google Scholar] [CrossRef] 
[8] Sottinen, T. (2001) Fractional Brownian Motion, Random Walks and Binary Market Models. Finance and Stochastics, 5, 343-355. [Google Scholar] [CrossRef] 
[9] Hu, Y.Z. (2005) Integral Transformations and Anticipative Calculus for Fractional Brownian Motions. emoirs of the American Mathematical Society, 175. [Google Scholar] [CrossRef] 
[10] Billingsley, P. (1968) Convergence of Probability Measures. In: Con-vergence of Probability Measures, John Wiley & Sons, Ltd., Hoboken.

为你推荐