Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-02-06T10:46:07.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Moderate deviation principle for a class of stochastic partial differential equations

Published online by Cambridge University Press:  24 March 2016

Parisa Fatheddin  and
Jie Xiong
Jie Xiong
Affiliation:
Department of Mathematics, FST, University of Macau, PO Box 3001, Macau, China.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two important population models: super-Brownian motion and the Fleming–Viot process.

Keywords

Moderate deviation principleFleming–Viot processstochastic partial differential equationsuper-Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 279 - 292
Copyright
Copyright © Applied Probability Trust 2016 

References

[1]Budhiraja, A., Dupuis, P. and Maroulas, V. (2008). Large deviations for infinite dimensional stochastic dynamical systems. Ann Prob. 36, 1390–1420. CrossRefGoogle Scholar
[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. (Corrigendum: 88 (2000), 175.) CrossRefGoogle Scholar
[3]Dembo, A. and Zeitouni, O. (2010). Large Deviations Techniques and Applications, 2nd edn. Springer, Berlin. CrossRefGoogle Scholar
[4]Dupuis, P. and Ellis, R. S. (1997). A Weak Convergence Approach to the Theory of Large Deviations. John Wiley, New York. CrossRefGoogle Scholar
[5]Fleischmann, K., Gärtner, J. and Kaj, I. (1996). A Schilder type theorem for super-Brownian motion. Canad. J. Math. 48, 542–568. CrossRefGoogle Scholar
[6]Fatheddin, P. (2015). Central limit theorem for a class of SPDEs. J. Appl. Prob. 52, 786–796. CrossRefGoogle Scholar
[7]Fatheddin, P. and Xiong, J. (2015). Large deviation principle for some measure-valued processes. Stoch. Process. Appl. 125, 970–993. CrossRefGoogle Scholar
[8]Feng, S. and Xiong, J. (2002). Large deviations and quasi-potential of a Fleming–Viot process. Electron. Commun. Prob. 7, 13–25. CrossRefGoogle Scholar
[9]Hong, W.-M. (2002). Moderate deviation for super-Brownian motion with super-Brownian immigration. J. Appl. Prob. 39, 829–838. CrossRefGoogle Scholar
[10]Hong, W.-M. (2008). Moderate deviations for the quenched mean of the super-Brownian motion with random immigration. Sci. China Ser. A 51, 343–350. CrossRefGoogle Scholar
[11]Kurtz, T. G. and Xiong, J. (1999). Particle representations for a class of nonlinear SPDEs. Stoch. Process. Appl. 83, 103–126. CrossRefGoogle Scholar
[12]Mitoma, I. (1985). An ∞-dimensional inhomogeneous Langevin's equation. J. Funct. Anal. 61, 342–359. CrossRefGoogle Scholar
[13]Schied, A. (1997). Moderate deviations and functional LIL for super-Brownian motion. Stoch. Process. Appl. 72, 11–25. CrossRefGoogle Scholar
[14]Xiong, J. (2013). Super-Brownian motion as the unique strong solution to an SPDE. Ann. Prob. 41, 1030–1054. CrossRefGoogle Scholar
[15]Yang, X. and Zhang, M. (2012). Moderate deviation for the single point catalytic super-Brownian motion. Acta Math. Sinica 28, 1799–1808. CrossRefGoogle Scholar
[16]Zhang, M. (2008). Some scaled limit theorems for an immigration super-Brownian motion. Sci. China Ser. A 51, 203–214. CrossRefGoogle Scholar