Moderate deviations for stochastic tidal dynamics equations with multiplicative Gaussian noise

References

• Lamb H. Hydrodynamics. New York: Dover Publications; 1932.
   Google Scholar
• Newton I. Philosophiae naturalis principia mathematica. 1687.
   Google Scholar
• Laplace PS. Recherches sur quelques points du syst‘eme du monde. Mem Acad Roy Sci Paris. 1775;88:75–182.
   Google Scholar
• Thomson W, Tait PG. Treatise on natural philosophy. Vol. Vol. I. Oxford: Clarendon Press; 1867.
   Google Scholar
• Poincaré H. Lecons de Mécanique Celeste. 3. Théroe des marées. Paris: Cauthier Villars; 1910.
   Google Scholar
• Marchuk GI, Kagan BA. Ocean tides. mathematical models and numerical experiments. Elmsford: Pergamon Press; 1984.
   Google Scholar
• Ipatova VM. Solvability of a tide dynamics model in adjacent seas. Russian J Numer Anal Math Model. 2005;20(1):67–79.
   Web of Science ®Google Scholar
• Manna U, Menaldi JL, Sritharan SS. Stochastic analysis of tidal dynamics equation. In: Sengupta AN, Sundar P, editors. Infinite dimensional stochastic analysis. Hackensack: World Scientic Publishers; 2008. p. 90–113.
   Google Scholar
• Mohan MT. On the two dimensional tidal dynamics system: stationary solution and stability. Applicable Anal. 2018. Available form: https://doi.org/https://doi.org/10.1080/00036811.2018.1546002
   Google Scholar
• Mohan MT. Dynamic programming and feedback analysis of the two dimensional Tidal dynamics system. ESAIM Control Optim Calculus Variations. 2020. Available form: https://doi.org/https://doi.org/10.1051/cocv/2020025
   Google Scholar
• Agarwal P, Manna U, Mukherjee D. Stochastic control of tidal dynamics equation with Lévy noise. Applied Mathe Optim. 2019;79:327–396.
   Web of Science ®Google Scholar
• Suvinthra M, Sritharan SS, Balachandran K. Large deviations for stochastic tidal dynamics equation. Commun Stoch Anal. 2015;9(4):477–502.
   Google Scholar
• Yin H. Stochastic analysis of backward tidal dynamics equation. Commun Stoch Anal. 2011;5(4):745–768.
   Google Scholar
• Freidlin MI, Wentzell AD. Random perturbations of dynamical systems. New York: Springer; 1984.
   Google Scholar
• Cerrai S, Röckner M. Large deviations for stochastic reaction–diffusion systems with multiplicative noise and non-Lipshitz reaction term. Ann Probab. 2004;32(1B):1100–1139.
   Web of Science ®Google Scholar
• Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Dembo A, Zeitouni O. Large deviations techniques and applications. New York: Springer; 2000.
   Google Scholar
• Faris WG, Jona-Lasinio G. Large fluctuations for a nonlinear heat equation with noise. J Phys Math General. 1982;15(10):3025–3055.
   Google Scholar
• Manna U, Mohan MT. Large deviations for the shell model of turbulence perturbed by Lévy noise. Commun Stoch Anal. 2013;7(1):39–63.
   Google Scholar
• Swiech A. A PDE approach to large deviations in Hilbert Spaces. Stoch Process Appl. 2009;119(4):1081–1123.
   Web of Science ®Google Scholar
• Budhiraja A, Dupuis P. A variational representation for positive functionals of infinite dimensional Brownian motion. Probab Math Stat. 2000;20(1):39–61.
   Google Scholar
• Foondun M, Setayeshgar L. Large deviations for a class of semilinear stochastic partial differential equations. Stat Probab Lett. 2017;121:143–151.
   Web of Science ®Google Scholar
• Haseena A, Suvinthra M, Annapoorani N. On large deviations of stochastic integrodifferential equations with Brownian motion. Discontin Nonlinear Complex. 2017;6(3):281–294.
   Google Scholar
• Haseena A, Suvinthra M, Annapoorani N. Large deviations for stochastic integrodifferential equations of the Itô type with multiple randomness. Filomat. 2018;32(2):473–487.
   Web of Science ®Google Scholar
• Sritharan SS, Sundar P. Large deviations for the two dimensional Navier–Stokes equations with multiplicative noise. Stoch Process Appl. 2006;116(11):1636–1659.
   Web of Science ®Google Scholar
• Suvinthra M, Balachandran K. Large deviations for the stochastic predator-prey model with nonlinear functional response. J Appl Probab. 2017;54(2):507–521.
   Web of Science ®Google Scholar
• Li Y, Wang R, Yao N, et al. A moderate deviation principle for stochastic Volterra equation. Stat Probab Lett. 2017;122:79–85.
   Web of Science ®Google Scholar
• Zheng W, Zhai J, Zhang T. Moderate deviations for stochastic models of two dimensional second grade fluids. Stochast Dyn. 2018;18(3):1850026.
   Web of Science ®Google Scholar
• Altug Y, Wagner AB. Moderate deviations in channel coding. IEEE Trans Inform Theory. 2014;60(8):4417–4426.
   Web of Science ®Google Scholar
• Chen X. Probabilities of moderate deviations for independent random vectors in a Banach space. Chinese J Appl Probab Stat. 1991;7:24–33.
   Google Scholar
• De Acosta A. Moderate deviations and associated Laplace approximations for sums of independent random vectors. Trans Am Math Soc. 1992;329(1):357–375.
   Web of Science ®Google Scholar
• Dupuis P, Johnson D. Moderate deviations-based importance sampling for stochastic recursive equations. Adv Appl Probab. 2017;49(4):981–1010.
   Web of Science ®Google Scholar
• Guillin A, Liptser R. Examples of moderate deviation principle for diffusion processes. Discr Contin Dyn Syst Ser B. 2006;6(4):803–828.
   Web of Science ®Google Scholar
• Wu L. Moderate deviations of dependent random variables related to CLT. Ann Probab. 1995;23(1):420–445.
   Web of Science ®Google Scholar
• Wang R, Zhang T. Moderate deviations for stochastic reaction–diffusion equations with multiplicative noise. Potential Anal. 2015;42(1):99–113.
   Web of Science ®Google Scholar
• Wang R, Zhai J, Zhang T. A moderate deviation principle for 2-D stochastic Navier–Stokes equations. J Differ Equ. 2015;258(10):3363–3390.
   Web of Science ®Google Scholar
• Budhiraja A, Dupuis P, Ganguly A. Moderate deviation principles for stochastic differential equations with jumps. Ann Probab. 2016;44(3):1723–1775.
   Web of Science ®Google Scholar
• Cai Y, Wang S. Central limit theorem and moderate deviation principle for CKLS model with small random perturbation. Stat Probab Lett. 2015;98:6–11.
   Web of Science ®Google Scholar
• Dong Z, Xiong J, Zhai J, Zhang T. A moderate deviation principle for 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noises. J Funct Anal. 2017;272(1):227–254.
   Web of Science ®Google Scholar
• Fatheddin P, Xiong J. Moderate deviation principle for a class of stochastic partial differential equations. J Appl Probab. 2016;53(1):279–292.
   Web of Science ®Google Scholar
• Klebaner F, Lipster R. Moderate deviations for randomly perturbed dynamical systems. Stoch Process Appl. 1999;80(2):157–176.
   Web of Science ®Google Scholar
• Mohan MT. A central limit theorem and moderate deviation principle for the stochastic 2D Oldroyd model of order one. Stoch Partial Differ Equ: Anal Comput. 2020.
   Google Scholar
• Morse MR, Spiliopoulos K. Moderate deviations for systems of slow-fast diffusions. Asymptotic Anal. 2017;105(3–4):97–135.
   Web of Science ®Google Scholar
• Marchuk GI, Kagan BA. Dynamics of ocean tides. Dordrecht: Kluwer Academic Publishers; 1989.
   Google Scholar
• Ladyzhenskaya OA. The mathematical theory of viscous incompressible flow. New York: Gordon and Breach; 1969.
   Google Scholar
• Métivier M. Stochastic partial differential equations in infinite dimensional spaces. Pisa: Quaderni, Scuola Normale Superiore; 1988.
   Google Scholar
• Marinelli C, Röckner M. On the maximal inequalities of Burkholder, Davis and Gundy. Expo Math. 2016;34(1):1–26.
   Web of Science ®Google Scholar
• Ciarlet PG. Linear and nonlinear functional analysis with applications. Philadelphia,PA: SIAM Philadelphia; 2013.
   Google Scholar
• Allan G. Probability: a graduate course. 2nd ed. New York: Springer-Verlag; 2013.
   Google Scholar
• Röckner M, Schmuland B, Zhang X. Yamada-Watanabe theorem for stochastic evolution equations in infinite dimensions. Condensed Matter Phys. 2008;11(2):247–259.
   Web of Science ®Google Scholar
• Ondreját M. Uniqueness for stochastic evolution equations in Banach spaces. Dissert Math (Rozprawy Mat). 2004;426:63.
   Google Scholar
• Davis B. On the integrability of the martingale square function. Israel J Math. 1970;8(2):187–190.
   Web of Science ®Google Scholar
• Vaughn MT. Introduction to mathematical physics. Weinheim: WILEY-VCH Verlag GmbH & Co. KGaA; 2007.
   Google Scholar