Browse > Article
http://dx.doi.org/10.4134/BKMS.b160198

SOME LIMITING RESULTS OF REFLECTED ORNSTEIN-UHLENBECK PROCESSES WITH TWO-SIDED BARRIERS  

Zhu, Chenglian (School of Mathematical Science Huaiyin Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 573-581 More about this Journal
Abstract
Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are concerned with the study of asymptotic behaviours of parametric estimation for ergodic reflected Ornstein-Uhlenbeck processes with two-sided barriers. Moreover, we also focus on the relations between regulators and the local time process.
Keywords
reflected Ornstein-Uhlenbeck processes; maximum likelihood estimation; ergodic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. Ata, J. M. Harrison, and L. A. Shepp, Drift rate control of a Brownian processing system, Ann. Appl. Probab. 15 (2005), no. 2, 1145-1160.   DOI
2 J. P. N. Bishwal, Large deviations inequalities for the maximum likelihood estimator and the Bayes estimators in nonlinear stochastic differential equations, Statist. Probab. Lett. 43 (1999), no. 2, 207-215.   DOI
3 J. P. N. Bishwal, Parameter estimation in stochastic differential equations, Lecture Notes in Mathematics, vol. 1923, Springer, Berlin Heidelberg, New York, 2008.
4 L. Bo, D. Tang, Y. Wang, and X. Yang, On the conditional default probability in a regulated market: a structural approach, Quant. Finance 11 (2011), no. 12, 1695-1702.   DOI
5 L. Bo, Y. Wang, and X. Yang, Some integral functionals of reflected SDEs and their applications in finance, Quant. Finance 11 (2011), no. 3, 343-348.   DOI
6 S. D. Hanson, R. J. Myers, and J. H. Hilker, Hedging with futures and options under truncated cash price distribution, J. Agricultural Appl. Economics 31 (1999), 449-459.   DOI
7 L. Bo, Y. Wang, X. Yang, and G. Zhang, Maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes, J. Statist. Plann. Inference 141 (2011), no. 1, 588-596.   DOI
8 P. D. Feigin, Some comments concerning a curious singularity, J. Appl. Prob. 16 (1979), 440-444.   DOI
9 R. S. Goldstein and W. P. Keirstead, On the term structure of interest rates in the presence of reflecting and absorbing boundaries, DOI:10.2139/ssrn.10.2139/ssrn.19840(1997).
10 M. Harrison, Brownian Motion and Stochastic Flow Systems, John Wiley and Sons, New York, 1986.
11 Y. Hu, C. Lee, M. H. Lee, and J. Song, Parameter estimation for reflected Ornstein-Uhlenbeck processes with discrete observations, preprint, 2013.
12 Z. Y. Huang, Foundation in Stochastic Calculus, Science Press, Beijing (in Chinese), 2001.
13 H. Jiang and X. Dong, Parameter estimation for the non-stationary Ornstein-Uhlenbeck process with linear drift, Statist. Papers 56 (2015), no. 1, 257-268.   DOI
14 P. R. Krugman, Target zones and exchange rate dynamics, Quarterly J. Economics 106 (1991), 669-682.   DOI
15 Y. A. Kutoyants, Statiatical Inference for Ergodic Diffusion Processes, Springer, Lon-don, 2004.
16 V. Linetsky, On the transition densities for reflected diffusions, Adv. in Appl. Probab. 37 (2005), no. 2, 435-460.   DOI
17 D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer Verlag, Berlin, 1998.
18 P. L. Lions and A. S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), no. 4, 511-537.   DOI
19 B. L. S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Oxford University Press, New York, 1999.
20 P. E. Protter, Stochastic Integration and Differential Equations, Springer Verlag, Berlin, 2004.
21 L. M. Ricciardi and L. Sacerdote, On the probability densities of an Ornstein-Uhlenbeck process with a reflecting boundary, J. Appl. Probab. 24 (1987), no. 2, 355-369.   DOI
22 A. Ward and P. Glynn, A diffusion approximation for a Markovian queue with reneging, Queueing Syst. 43 (2003), no. 1-2, 103-128.   DOI
23 A. Ward and P. Glynn, Properties of the reflected Ornstein-Uhlenbeck process, Queueing Syst. 44 (2003), no. 2, 109-123.   DOI
24 A. Ward and P. Glynn, A diffusion approximation for a GI/GI/1 queue with balking or reneging, Queueing Syst. 50 (2005), no. 4, 371-400.   DOI
25 Q. Zang and L. Zhang, Parameter estimation for generalized diffusion processes with reflected boundary, Sci. China Math. 59 (2016), no. 6, 1163-1174.   DOI