ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNATEIN-UHLENBECK PROCESSES

doi:10.1016/S0252-9602(17)30004-8

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 316-328.doi: 10.1016/S0252-9602(17)30004-8

• Articles • Previous Articles Next Articles

ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNATEIN-UHLENBECK PROCESSES

Jingjun GUO¹, Chujin LI²

1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China;
2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2015-05-06 Revised:2016-05-06 Online:2017-04-25 Published:2017-04-25
Contact: Chujin LI,E-mail:lichujin@hust.edu.cn E-mail:lichujin@hust.edu.cn
Supported by:
The first author is supported by the National Natural Science Fundation of China (71561017), the Science and Technology Plan of Gansu Province (1606RJZA041), and the Youth Plan of Academic Talent of Lanzhou University of Finance and Economics; the second author is supported by the Fundamental Research Funds for the Central Universities (HUST2015QT005).

Abstract

Abstract:

In this article, we study the existence of collision local time of two independent d-dimensional fractional Ornstein-Uhlenbeck processes X_t^H1 and X_t^H2, with different parameters H_i ∈ (0,1), i=1,2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its' chaos expansion.

Key words: Collision local time, fractional Ornstein-Uhlenbeck processes, generalized white noise functionals, choas expansion

Jingjun GUO, Chujin LI. ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNATEIN-UHLENBECK PROCESSES[J].Acta mathematica scientia,Series B, 2017, 37(2): 316-328.

Trendmd

References

[1] Bender C. An Itô formula for generalized of a fractional Brownian motions with arbitrary Hurst parameter. Stoc Proces Appl, 2003, 104:81-106
[2] Biagini F, Hu Y, et al. Stochastic Calculus for Fractional Brownian Motion and Applications. London: Springer-Verlag, 2008
[3] Guo J, Xiao Y. On collision local time of two independent of subfractional Brownian motions. Computer Model Engin Scien, 2015, 109(6):519-536
[4] Hu Y, Nualart D. Regularity of renormalized self-intersection local time for fractional Brownian motion. Commun Inf Syst, 2007, 7(1):21-30
[5] Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Statis Proba Lette, 2010, 80:1030-1038
[6] Jiang Y, Wang Y. On the collision local time of fractional Brownian motions. Chin Ann Math, 2007, 28: 311-320
[7] Liu J, Peng Z, et al. On the self-intersection local time of subfractional Brownian motion. Abstr Appl Analy, 2012(2012):1-27
[8] Maslowski B, Tudor C. Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process. Bull Sci Math, 2013, 137:880-901
[9] Nualart D, Ortiz-Latorre S. Intersection local time for two independent fractional Brownian motions. J Theor Prob, 2007, 20:759-767
[10] Oliveira M, Silva J, et al. Intersection local times of independent fractional Brownian motions as generalized white noise functionals. Acta Appl Math, 2011, 113(1):17-39
[11] Rifo L, Torres S, et al. Comparative estimation for discrete fractional Ornstein-Uhlenbeck process. Stoch Models, 2013, 29(3):291-305
[12] Shen G, Yin X, Yan L. Least squares estimation for Ornstein-Uhlenbeck processes driven by the weighted fractional Brownian motion. Acta Mathemtica Scientia, 2016, 36B(2):394-408
[13] Shen G, Zhu D, et al. The local time of the fractional Ornstein-Uhlenbeck process. Abstr Appl Analy, 2013(2013):1-9
[14] Yan L, Shen G. On the collision local time of sub-fractional Brownian motions. Statis Prob Lette, 2010, 80:296-308
[15] Yan L, Tian M. On the local times of fractional Ornstein-Uhlenbeck process. Lette Math Phys, 2005, 73(3): 209-220
[16] Wang X, Guo J, et al. Collision local times of two independent fractional Brownian motions. Front Math in China, 2011, 6(2):325-338
[17] Wu D, Xiao Y. Regularity of intersection local times of fractional Brownian motions. J Theor Prob, 2010, 23(4):972-1001

ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNATEIN-UHLENBECK PROCESSES

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 0

Metrics

Comments

Recommended 1