Journal of Applied Nonlinear Dynamics
Large Deviations for Nonlinear Itô Type Stochastic Integrodifferential Equations
Journal of Applied Nonlinear Dynamics 6(1) (2017) 115  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 FreidlinWentzell 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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