JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 19-26.doi: 10.6040/j.issn.1671-9352.0.2014.234

Previous Articles     Next Articles

Power variation of weighted-fractional Brownian motion and application

DENG Long-juan, ZHU Dong-jin, SHEN Guang-jun   

  1. Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui, China
  • Received:2014-05-27 Revised:2015-01-13 Online:2015-06-20 Published:2015-07-31

PDF (PC)

734

Abstract: The power variation of weighted-fractional Brownian motion was considened by using its stochastic calculus representation. As an application, the estimate of parameter b was obtainted.

Key words: weighted-fractional Brownian motion, power variation, strongly consistent

CLC Number: 

  • O211.6
[1] MISHURA Y. Stochasic calculus for fractional Brownian motion and related processes[M]. New York: Springer-Verlag, 2008.
[2] BOJDECKI T, GOROSTIZA L G, TALARCZYK A. Self-similar stable processes arising from high density limits of occupation times of particle systems[J]. Potent Anal, 2008, 28:71-103.
[3] LÉVY P. Le movement Brownien plan[J]. Amer J Math, 1940, 62: 487-550.
[4] KLEIN R, GINÉ E. On quadratic variation of processes with Gaussian increments[J]. Ann Probab, 1975, 3:716-721.
[5] MARCUS M B, ROSEN J. p-variation of the local times of symmetric stable processes and of Gaussian Processes with stationary increments[J]. Ann Probab, 1992, 20:1685-1713.
[6] WANG Wensheng. On p-variational of bifractional Brownian motion[J]. Appl Math J Chinese Univ, 2011, 26(2):127-141.
[7] YAN Litan, WANG Zhi, JING Huiting. Some path properties of weighted-fractional Brownian motion[J]. Stochastics: An International Journal of Probability and Stochastic Processes, 2014, 86(5):721-758.
[8] SHEN Guangjun, YAN Litan, CUI Jing. Berry-Esséen bounds and almost sure CLT for quadratic variation of weighted fractional Brownian motion[J]. Journal of Inequalities and Applications, 2013, 2013:275.
[9] CSÁKI E, CSÖRG?M, SHAO Q M. Fernique type inequalities and moduli of continuity for l2-valued Ornstein-Uhlenbeck processes[J]. Ann Inst Henri Poincaré Probab Statist, 1992, 28: 479-517.
[10] TALAGRAND M. Hausdorff measure of trajectories of multiparameter fractional Brownian motion[J]. Ann Probab, 1995, 23:767-775.
[11] ADLER R J. An introduction to continuity extrema, and related topics general Gaussian processes[M]. IMS Bardour-Rice-Strawderman, 1990.
[1] MA Ming, BIAN Li-na, LIU Hua. Low order moments of self-excited filtered Poisson processes based on joint distribution of event points [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 55-58.
[2] XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.
[3] ZHANG Ya-juan, LYU Yan. Approximation of stochastic vibration equations with variable damping [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 59-65.
[4] CUI Jing, LIANG Qiu-ju. Existence and controllability of nonlocal stochastcic integro-differential equations driven by fractional Brownian motion [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 81-88.
[5] RONG Wen-ping, CUI Jing. μ-pseudo almost automorphic solutions for a class of stochastic evolution equations under non-Lipschitz conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 64-71.
[6] ZHANG Jie-song. Diffusion approximation and optimal investment for modern risk model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(5): 49-57.
[7] YANG Xu, LI Shuo. Comparison theorem for backward doubly stochastic differential equations driven by white noises and Poisson random measures [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 26-29.
[8] ZHANG Chun-yan, HAO Sheng-nan, FENG Li-chao. Stochastic suppression on explosive solutions of a class of nonlinear impulsive differential systems by noise [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 29-36.
[9] FEI Shi-long, BAI Yao-qian. A class of random walks in a random environment with singular jumps [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(11): 119-126.
[10] CHEN Jie, LÜ Yu-hua. Discounted penalty function for a thinning risk model with dividend [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(09): 78-83.
[11] FANG Rui, MA Jiao-jiao, FAN Sheng-jun. A stability theorem for solutions of a class of backward stochastic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 39-44.
[12] WANG Cui-lian, LIU Xiao. On a periodic dividend problems in the Brownian motion model with investment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 74-81.
[13] WANG Chun-sheng, LI Yong-ming. Stability of neutral stochastic differential equations with some variable delays [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 82-87.
[14] ZHANG Quan, HAN Yang, GUAN Bao-ling, LI Yan-jun. Reliability analysis of a warm standby repairable system with unreliable transfer switch [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 62-65.
[15] ZHAO Jie, SHI Yu-feng. Backward stochastic Volterra integral equations with general martingales [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 63-68.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd