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

Part of: Markov processes Parametric inference

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
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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
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 14
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

Abi-ayad, I. and Mourid, T. (2018). Parametric estimation for non recurrent diffusion processes. Statist. Prob. Lett. 141, 96–102.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Dietz, H. M. (2001). Asymptotic behaviour of trajectory fitting estimators for certain non-ergodic SDE. Statist. Infer. Stoch. Process. 4, 249–258.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Linetsky, V. (2005). On the transition densities for reflected diffusions. Adv. Appl. Prob. 37, 435–460.CrossRefGoogle Scholar
Lions, P. L. and Sznitman, A. S. (1984). Stochastic differential equations with reflecting boundary condition. Commun. Pure. Appl. Math. 37, 511–537.CrossRefGoogle 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.CrossRefGoogle Scholar
Ward, A. R. and Glynn, P. W. (2003). A diffusion approximation for a Markovian queue with reneging. Queueing Systems 43, 103–128.CrossRefGoogle 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.CrossRefGoogle Scholar
Whitt, W. (2002). Stochastic-Process Limits. Springer, New York.CrossRefGoogle Scholar
Zang, Q. P. and Zhang, L. X. (2016). Parameter estimation for generalized diffusion processes with reflected boundary. Sci. China Math. 59, 1163–1174.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar