Hostname: page-component-6565fbc58-8ndt2 Total loading time: 0 Render date: 2026-03-13T02:50:38.833Z Has data issue: false hasContentIssue false
  • English
  • Français

Trajectory fitting estimation for reflected stochastic linear differential equations of a large signal

Part of: Parametric inference Markov processes

Published online by Cambridge University Press:  31 October 2023

Xuekang Zhang Open the ORCID record for Xuekang Zhang [Opens in a new window]  and
Huisheng Shu
Xuekang Zhang*
Affiliation:
Anhui Polytechnic University
Huisheng Shu*
Affiliation:
Donghua University
*
*Postal address: School of Mathematics-Physics and Finance, and Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China. Email address: xkzhang@ahpu.edu.cn
**Postal address: College of Science, Donghua University, Shanghai, 201620, China. Email address: hsshu@dhu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE).

Keywords

trajectory fitting estimatorreflected stochastic linear differential equationlarge signalconsistencyasymptotic distributions

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 60J60: Diffusion processes

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 3 , September 2024 , pp. 741 - 754
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abi-ayad, I. and Mourid, T. (2018). Parametric estimation for non recurrent diffusion processes. Statist. Prob. Lett. 141, 96–102.10.1016/j.spl.2018.05.024CrossRefGoogle Scholar
Bo, L. J., Tang, D., Wang, Y. J. and Yang, X. W. (2011). On the conditional default probability in a regulated market: a structural approach. Quant. Finance 11, 1695–1702.10.1080/14697680903473278CrossRefGoogle Scholar
Bo, L. J., Wang, Y. J. and Yang, X. W. (2010). Some integral functionals of reflected SDEs and their applications in finance. Quant. Finance 11, 343–348.10.1080/14697681003785926CrossRefGoogle Scholar
Bo, L. J., Wang, Y. J., Yang, X. W. and Zhang, G. N. (2011). Maximum likelihood estimation for reflected Ornstein–Uhlenbeck processes. J. Statist. Planning Infer. 141, 588–596.10.1016/j.jspi.2010.07.001CrossRefGoogle Scholar
Dietz, H. M. (2001). Asymptotic behaviour of trajectory fitting estimators for certain non-ergodic SDE. Statist. Infer. Stoch. Process. 4, 249–258.10.1023/A:1012254332474CrossRefGoogle Scholar
Dietz, H. M. and Kutoyants, Y. A. (1997). A class of minimum-distance estimators for diffusion processes with ergodic properties. Statist. Decisions 15, 211–227.Google Scholar
Dietz, H. M. and Kutoyants, Y. A. (2003). Parameter estimation for some non-recurrent solutions of SDE. Statist. Decisions 21, 29–45.10.1524/stnd.21.1.29.20321CrossRefGoogle Scholar
Han, Z., Hu., Y. Z. and Lee, C. (2016). Optimal pricing barriers in a regulated market using reflected diffusion processes. Quant. Finance 16, 639–647.10.1080/14697688.2015.1034163CrossRefGoogle Scholar
Harrison, M. (1986). Brownian Motion and Stochastic Flow Systems. John Wiley, New York.Google Scholar
Hu, Y. Z., Lee, C., Lee, M. H. and Song, J. (2015). Parameter estimation for reflected Ornstein–Uhlenbeck processes with discrete observations. Statist. Infer. Stoch. Process. 18, 279–291.10.1007/s11203-014-9112-7CrossRefGoogle Scholar
Jiang, H. and Xie, C. (2016). Asymptotic behaviours for the trajectory fitting estimator in Ornstein–Uhlenbeck process with linear drift. Stochastics 88, 336–352.10.1080/17442508.2015.1066378CrossRefGoogle Scholar
Jiang, H. and Yang, Q. S. (2022). Moderate deviations for drift parameter estimations in reflected Ornstein–Uhlenbeck process. J. Theoret. Prob. 35, 1262–1283.10.1007/s10959-021-01096-3CrossRefGoogle Scholar
Karatzas, I. and Shreve, S. (1991). Brownian Motion and Stochastic Calculus. Springer, New York.Google Scholar
Krugman, P. R. (1991). Target zones and exchange rate dynamics. Quart. J. Econom. 106, 669–682.10.2307/2937922CrossRefGoogle Scholar
Kutoyants, Y. A. (1991). Minimum distance parameter estimation for diffusion type observations. C. R. Acad. Sci. Paris 312, 637–642.Google Scholar
Kutoyants, Y. A. (2004). Statistical Inference for Ergodic Diffusion Processes. Springer, Berlin.10.1007/978-1-4471-3866-2CrossRefGoogle Scholar
Linetsky, V. (2005). On the transition densities for reflected diffusions. Adv. Appl. Prob. 37, 435–460.10.1239/aap/1118858633CrossRefGoogle Scholar
Lions, P. L. and Sznitman, A. S. (1984). Stochastic differential equations with reflecting boundary condition. Commun. Pure. Appl. Math. 37, 511–537.10.1002/cpa.3160370408CrossRefGoogle Scholar
Ricciardi, L. M. and Sacerdote, L. (1987). On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary. J. Appl. Prob. 24, 355–369.10.2307/3214260CrossRefGoogle Scholar
Ward, A. R. and Glynn, P. W. (2003). A diffusion approximation for a Markovian queue with reneging. Queueing Systems 43, 103–128.10.1023/A:1021804515162CrossRefGoogle Scholar
Ward, A. R. and Glynn, P. W. (2005). A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Systems 50, 371–400.10.1007/s11134-005-3282-3CrossRefGoogle Scholar
Whitt, W. (2002). Stochastic-Process Limits. Springer, New York.10.1007/b97479CrossRefGoogle Scholar
Zang, Q. P. and Zhang, L. X. (2016). Parameter estimation for generalized diffusion processes with reflected boundary. Sci. China Math. 59, 1163–1174.10.1007/s11425-015-5112-3CrossRefGoogle Scholar
Zang, Q. P. and Zhang, L. X. (2016). A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes. J. Appl. Prob. 53, 22–32.10.1017/jpr.2015.5CrossRefGoogle Scholar
Zang, Q. P. and Zhang, L. X. (2019). Asymptotic behaviour of the trajectory fitting estimator for reflected Ornstein–Uhlenbeck processes. J. Theoret. Prob. 32, 183–201.10.1007/s10959-017-0796-7CrossRefGoogle Scholar
Zang, Q. P. and Zhu, C. L. (2016). Asymptotic behaviour of parametric estimation for nonstationary reflected Ornstein–Uhlenbeck processes. J. Math. Anal. Appl. 444, 839–851.10.1016/j.jmaa.2016.06.067CrossRefGoogle Scholar
Zhang, X. K. and Shu, H. S. (2023). Maximum likelihood estimation for the reflected stochastic linear system with a large signal. Brazilian J. Prob. Statist. 37, 351–364.10.1214/23-BJPS571CrossRefGoogle Scholar