×
Fatheddin, Parisa

Central limit theorem for a class of SPDEs. (English) Zbl 1327.60058

J. Appl. Probab. 52, No. 3, 786-796 (2015).
Summary: In this paper, we establish the central limit theorem for a class of stochastic partial differential equations and as an application derive this theorem for two widely studied population models: super-Brownian motion and the Fleming-Viot process.

Cited in 3 Documents

MSC:

60F05 Central limit and other weak theorems
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J68 Superprocesses
60J65 Brownian motion
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

central limit theorem; stochastic partial differential equations; super-Brownian motion; Fleming-Viot process
PDF BibTeX XML Cite
\textit{P. Fatheddin}, J. Appl. Probab. 52, No. 3, 786--796 (2015; Zbl 1327.60058)
Full Text: DOI arXiv Euclid
  • logo of hbz
  • logo of WorldCat

References:

[1] Billingsley, P. (1968). Convergence of Probability Measures . John Wiley, New York. · Zbl 0172.21201
[2] Dawson, D. A. and Feng, S. (1998). Large deviations for the Fleming-Viot process with neutral mutation and selection. Stoch. Process. Appl. 77, 207-232. (Correction: 88 (2000), 175.) · Zbl 0934.60024
[3] Etheridge, A. M. (2000). An Introduction to Superprocesses (Univ. Lecture Ser. 20 ). American Mathematical Society, Providence, RI. · Zbl 0971.60053
[4] Fatheddin, P. and Xiong, J. (2015). Large deviation principle for some measure-valued processes. Stoch. Proc. Appl. 125, 970-993. · Zbl 1325.60024
[5] Fatheddin, P. and Xiong, J. (2015). Moderate deviation principle for a class of SPDEs. To Appear in J. Appl. Prob. · Zbl 1325.60024
[6] Feng, S. and Xiong, J. (2002). Large deviations and quasi-potential of a Fleming-Viot process. Electron. Commun. Prob. 7, 13-25. · Zbl 1008.60048
[7] Hong, W. (1998). Central limit theorem for the occupation time of catalytic super-Brownian motion. Chinese Sci. Bull. 43, 2035-2040. · Zbl 0988.60006
[8] Hong, W. (2002). Longtime behavior for the occupation time process of a super-Brownian motion with random immigration. Stoch. Process. Appl. . 102, 43-62. · Zbl 1075.60568
[9] Hong, W. (2005). Quenched mean limit theorems for the super-Brownian motion with super-Brownian immigration. Infin. Dimens. Anal. Quantum Prob. Relat. Top. 8, 383-396. · Zbl 1078.60066
[10] Hong, W.-M. and Li, Z.-H (1999). A central limit theorem for super-Brownian motion with super-Brownian immigration. J. Appl. Prob. 36, 1218-1224. · Zbl 0982.60087
[11] Hong, W. and Li, Z. (2001). Fluctuations of a super-Brownian motion with randomly controlled immigration. Statist. Prob. Lett. 51, 285-291. · Zbl 0977.60090
[12] Hong, W. and Wang, Z. (2000). Immigration process in catalytic medium. Sci. China Ser. A 43, 59-64. · Zbl 0956.60095
[13] Hong, W. and Zeitouni, O. (2007). A quenched CLT for super-Brownian motion with random immigration. J. Theoret. Prob. 20, 807-820. · Zbl 1132.60302
[14] Iscoe, I. (1986). A weighted occupation time for a class of measure-valued branching processes. Prob. Theory Relat. Fields 71, 85-116. · Zbl 0555.60034
[15] Lee, T.-Y and Remillard, B. (1995). Large deviations for the three-dimensional super-Brownian motion. Ann. Prob. 23, 1755-1771. · Zbl 0852.60004
[16] Li, Z. (1999). Some central limit theorems for super Brownian motion. Acta Math. Sci. 19, 121-126. · Zbl 0938.60091
[17] Mitoma, I. (1983). Tightness of probabilities on \(\mathcal{C}([0,1]; \mathcal{S}')\) and \(D([0,1]; \mathcal{S}')\). Ann. Prob. 11, 989-999. · Zbl 0527.60004
[18] Schied, A. (1997). Moderate deviations and functional LIL for super-Brownian motion. Stoch. Process. Appl. 72, 11-25. · Zbl 0942.60017
[19] Whitt, W. (2002). Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues . Springer, New York. · Zbl 0993.60001
[20] Xiong, J. (2013). Super-Brownian motion as the unique strong solution to an SPDE. Ann. Prob. 41, 1030-1054. · Zbl 1266.60119
[21] Zhang, M. (2008). Some scaled limit theorems for an immigration super-Brownian motion. Sci. China Ser. A 51, 203-214. · Zbl 1141.60050
[22] Zhang, M. (2009). On the weak convergence of super-Brownian motion with immigration. Sci. China Ser. A 52, 1875-1886. · Zbl 1179.60057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.