ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

On Large Deviations of Stochastic Integrodifferential Equations with Brownian Motion

Discontinuity, Nonlinearity, and Complexity 6(3) (2017) 281--294 | DOI:10.5890/DNC.2017.09.003

A. Haseena$^{1}$ , M. Suvinthra$^{2}$ , N. Annapoorani$^{2}$

1Department of Mathematics, Government College Chittur, Palakkad, 678104, India

2Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

Abstract

In this paper, a Freidlin-Wentzell type large deviation principle is established for the stochastic integrodifferential equation driven by finite dimensional Brownian motion. Both the additive and multiplicative noise cases are considered here. Large deviation principle for additive noise case is established via contraction principle whilst weak convergence approach is employed to obtain the same for the multiplicative noise case.

Acknowledgments

The authors are thankful to Prof. K. Balachandran (UGC-BSR Faculty, Department of Mathematics, Bharathiar University, Coimbatore) for several improvements he suggested throughout the preparation of the paper. Also we would like to thank the reviewers for their valuable comments which helped us a lot in enhancing the quality of the paper.

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