Large deviation principle for the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise

References

• Varadhan, S. R. S. (1984). Large Deviations and Applications. Philadelphia: SIAM.
   Google Scholar
• Dembo, A., Zeitouni, O. (2000). Large Deviations Techniques and Applications. New York, NY: Springer- Verlag.
   Google Scholar
• Deuschel, J. D., Stroock, D. W. (1989). Large Deviations. San Diego, CA: Academic Press.
   Google Scholar
• Freidlin, M. I., Wentzell, A. D. (1984). Random Perturbations of Dynamical Systems. New York, NY: Springer.
   Google Scholar
• Dupuis, P., Ellis, R. S. (1997). A Weak Convergence Approach to the Theory of Large Deviations. New York, NY: John Wiley & Sons.
   Google Scholar
• Fleming, W. H. (1985). A stochastic control approach to some large deviations problems. Lect. Notes Math. 1119:52–66.
   Web of Science ®Google Scholar
• Budhiraja, A., Dupuis, P. (2000). A variational representation for positive functionals of infinite dimensional Brownian motion. Probab. Math. Statist. 20(1):39–61.
   Google Scholar
• Amali Paul Rose, G., Suvinthra, M., Balachandran, K.   (2019). Large deviation principle for stochastic generalized KdV equation with additive noise. Indian J Indust. Appl. Math. 10(2):178–193. DOI: 10.5958/1945-919X.2019.00033.1.
   Google Scholar
• Amali Paul Rose, G., Suvinthra, M., Balachandran, K. (2021). Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise. Nonlinear Anal. Model Control. 26(4):642–660. DOI: 10.15388/namc.2021.26.24178.
   Web of Science ®Google Scholar
• Boulanba, L., Mellouk, M. (2020). Large deviations for a stochastic Cahn–Hilliard equation in Hölder norm. Infin. Dimens. Anal. Quantum Probab. Relat. Top. . 23(02):2050010. DOI: 10.1142/S0219025720500101.
   Google Scholar
• Budhiraja, A., Dupuis, P., Maroulas, V. (2008). Large deviations for infinite dimensional stochastic dynamical systems. Ann. Probab. 36(4):1390–1420. DOI: 10.1214/07-AOP362.
   Web of Science ®Google Scholar
• Mandelbrot, B. B., Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10(4):422–437. DOI: 10.1137/1010093.
   Web of Science ®Google Scholar
• Alòs, E., Mazet, E., Nualart, D. (2001). Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29(2):766–801. DOI: 10.1214/aop/1008956692.
   Web of Science ®Google Scholar
• Capitaine, M., Donati-Martin, C. (2001). The Lévy area process for the free Brownian motion. J. Funct. Anal. 179(1):153–169. DOI: 10.1006/jfan.2000.3679.
   Web of Science ®Google Scholar
• Coutin, L., Qian, Z. (2002). Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Relat. Fields . 122(1):108–140. DOI: 10.1007/s004400100158.
   Web of Science ®Google Scholar
• Decreusefond, L., Üstünel, A.S. (1999). Stochastic analysis of the fractional Brownian motion. Potent. Anal. 10(2):177–214. DOI: 10.1023/A:1008634027843.
   Web of Science ®Google Scholar
• Karali, G., Katsoulakis, M. A. (2007). The role of multiple microscopic mechanisms in cluster interface evolution. J. Differ. Equ. 235(2):418–438. DOI: 10.1016/j.jde.2006.12.021.
   Web of Science ®Google Scholar
• Antonopoulou, D. C., Karali, G., Millet, A. (2016). Existence and regularity of solution for a stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion. J. Differ. Equ. 260(3):2383–2417. DOI: 10.1016/j.jde.2015.10.004.
   Web of Science ®Google Scholar
• Antonopoulou, D. C., Farazakis, D., Karali, G. (2018). Malliavin calculus for the stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion. J. Differ. Equ. 265(7):3168–3211. DOI: 10.1016/j.jde.2018.05.004.
   Web of Science ®Google Scholar
• Jiang, Y. M., Shi, K. H., Wang, Y. J. (2010). Large deviation principle for the fourth-order stochastic heat equations with fractional noises. Acta Math. Sin-English. Ser. 26(1):89–106. DOI: 10.1007/s10114-010-7366-6.
   Web of Science ®Google Scholar
• Maroulas, V., Xiong, J. (2013). Large deviations for optimal filtering with fractional Brownian motion. Stoch. Process. Appl. 123(6):2340–2352. DOI: 10.1016/j.spa.2013.02.012.
   Web of Science ®Google Scholar
• Yan, L., Yin, X. (2018). Large deviation principle for a space-time fractional stochastic heat equation with fractional noise. Fract. Calcul. Appl. Anal. 21(2):462–485. DOI: 10.1515/fca-2018-0026.
   Web of Science ®Google Scholar
• Xia, D., Yan, L., Yin, X. (2018). On a semilinear double fractional heat equation driven by fractional Brownian sheet. J. Appl. Anal. Comput. 8(1):202–228.
   Google Scholar
• Cardon-Weber, C. (2001). Cahn-Hilliard stochastic equation: Existence of the solution and of its density. Bernoulli. 7(5):777–816. DOI: 10.2307/3318542.
   Web of Science ®Google Scholar
• Bo, L., Jiang, Y., Wang, Y. (2008). Stochastic Cahn–Hilliard equation with fractional noise. Stoch. Dyn. 8(4):643–665. DOI: 10.1142/S0219493708002500.
   Web of Science ®Google Scholar
• Nualart, D., Ouknine, Y. (2004). Regularization of quasilinear heat equations by a fractional noise. Stoch. Dyn. 04(02):201–221. DOI: 10.1142/S0219493704001012.
   Google Scholar
• Mémin, J., Mishura, Y., Valkeila, E. (2001). Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion. Stat. Probab. Lett. 51(2):197–206. DOI: 10.1016/S0167-7152(00)00157-7.
   Web of Science ®Google Scholar
• Walsh, J. B. (1984). An introduction to stochastic partial differential equations. Lect. Notes Math. 1180:265–439.
   Web of Science ®Google Scholar
• Bryc, W. (1990). Large deviations by the asymptotic value method. In Diffusion Processes and Related Problems in Analysis. Boston, MA: Birkhäuser, pp. 447–472.
   Google Scholar
• Ikeda, N., Watanabe, S. (2014). Stochastic Differential Equations and Diffusion Processes. New York, NY: Elsevier.
   Google Scholar
• Bally, V., Millet, A., Sanz-Sole, M. (1995). Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations. Ann. Probab. 23(1):178–222. DOI: 10.1214/aop/1176988383.
   Web of Science ®Google Scholar