Exponential inequalities for exit times for two dimensional stochastic tidal dynamics equations

Abstract

In this work, we consider two dimensional stochastic tidal dynamics equations in bounded domains. We establish the exponential estimates on certain exit times associated with the solution trajectory of the tidal dynamics system. Using contraction principle, we study these exponential estimates of exit times in the context of a Wentzell-Freidlin type large deviations principle.

Keywords:

• Tidal dynamics system
• exponential estimates
• contraction principle
• large deviation principle

Mathematics Subject Classification (2010):

• 35Q35
• 60H15
• 60G15

Acknowledgements

M. T. Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110). The author sincerely would like to thank the reviewers for their valuable comments and suggestions, which helped to improve the manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Department of Science and Technology, India.