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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Large Deviations for Nonlinear Itô Type Stochastic Integrodifferential Equations

Journal of Applied Nonlinear Dynamics 6(1) (2017) 1--15 | DOI:10.5890/JAND.2017.03.001

M. Suvinthra; K. Balachandran

Department of Mathematics, Bharathiar University, Coimbatore 641 046, India

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Abstract

In this work, we consider a nonlinear Itô type stochastic integrodifferential equation and study the Freidlin-Wentzell type large deviation principle for its solution processes. The weak convergence approach is employed to establish the Laplace principle which in turn is equivalent to the large deviation principle. The compactness criterion is verified by means of sequential compactness of solutions of the associated controlled equation. The weak convergence result is asserted via solutions of the controlled equation with stochastic perturbation. Finally, examples are included to illustrate the theory.

Acknowledgments

The first author would like to thank the Department of Science and Technology, New Delhi for their financial support under the INSPIRE Fellowship Scheme.

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