Abstract
We prove a large deviation principle of Freidlin–Wentzell type for multivalued stochastic differential equations with monotone drifts that in particular contain a class of SDEs with reflection in a convex domain.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, R.F., Orey, S.: Small random perturbation of dynamical systems with reflecting boundary. Nagoya Math. J. 60, 189–216 (1976)
Boué, M., Dupuis, P.: A variational representation for certain functionals of Brownian motion. Ann. Probab. 26(4), 1641–1659 (1998)
Budhiraja, A., Dupuis, P.: A variational representation for positive functionals of infinite dimensional Brownian motion. Probab. Math. Stat. 20(1), 39–61 (2000). Acta Univ. Wratislav. 2246, 39–61 (2000)
Budhiraja, A., Dupuis, P., Maroulas, V.: Large deviations for infinite dimensional stochastic dynamical systems. Ann. Probab. 36(4), 1390–1420 (2008)
Cépa, E.: Équations différentielles stochastiques multivoques. In: Sém. Prob. XXIX, Lect. Notes in Math., vol. 1613, pp. 86–107. Springer, Berlin (1995)
Cépa, E.: Problème de Skorohod multivoque. Ann. Probab. 26(2), 500–532 (1998)
Deuschel, J.D., Stroock, D.W.: Large Deviations. Academic Press, Boston (1988)
Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York (1997)
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, 2nd edn. Kodansha/North-Holland, Tokyo/Amsterdam (1989)
Liu, W.: Large deviations for stochastic evolution equations with small multiplicative noise. Appl. Math. Optim. 61, 27–56 (2010)
Ren, J., Zhang, X.: Freidlin–Wentzell’s large deviations for homeomorphism flows of non-Lipschitz SDEs. Bull. Sci. Math. 2 Ser. 129(8), 643–655 (2005)
Ren, J., Zhang, X.: Freidlin–Wentzell’s large deviations for stochastic evolution equations. J. Funct. Anal. 254, 3148–3172 (2008)
Xu, S.: Explicit solutions for multivalued stochastic differential equations. Stat. Probab. Lett. 78, 2281–2292 (2008)
Zhang, X.: Skorohod problem and multivalued stochastic evolution equations in Banach spaces. Bull. Sci. Math. 131(2), 175–217 (2007)
Zhang, X.: Euler schemes and large deviations for stochastic Volterra equations with singular kernels. J. Differ. Equ. 224, 2226–2250 (2008)
Zhang, X.: A variational representation for random functionals on abstract Wiener spaces. J. Math. Kyoto Univ. 49(3), 475–490 (2009)
Zhang, X.: Stochastic Volterra equations in Banach spaces and stochastic partial differential equations. J. Funct. Anal. 258, 1361–1425 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by NSF of China (No. 10871215).
Rights and permissions
About this article
Cite this article
Ren, J., Xu, S. & Zhang, X. Large Deviations for Multivalued Stochastic Differential Equations. J Theor Probab 23, 1142–1156 (2010). https://doi.org/10.1007/s10959-009-0274-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10959-009-0274-y