Moderate deviations for a class of semilinear SPDE with fractional noises

References

• Albeverio, S., Rüdiger, B., Wu, J. L. (2000). Invariant measures and symmetry property of Lévy type operators. Potential Anal. 13(2):147–168. DOI: 10.1023/A:1008705820024.
   Web of Science ®Google Scholar
• Azencott, R. (1980). Grands deviations et applications, Ecole d’Ete de Probabilities de Saint Flour VIII-1978. In: Lectures Notes in Math, vol. 774. Berlin: Springer-Verlag, pp. 1–176.
   Google Scholar
• Baier, U., Freidlin, M. I. (1977). Theorems on large deviations and stability under random perturbations. Dokl. Akad. Nauk. USSR. 235:253–256.
   Google Scholar
• Bally, V., Millet, A., Sanz-Solé, 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
• Cardon-Weber, C. (1999). Large deviations for a Burgers’-type SPDE. Stoch. Process. Appl. 84(1):53–70. DOI: 10.1016/S0304-4149(99)00047-2.
   Web of Science ®Google Scholar
• Chenal, F., Millet, A. (1997). Uniform large deviations for parabolic SPDEs and applications. Stoch. Process. Appl. 72(2):161–186. DOI: 10.1016/S0304-4149(97)00091-4.
   Web of Science ®Google Scholar
• Cramér, H. (1938). Sur un nouveau théorèm limite de la théorie des probabilités. Actual. Sci. Ind. 736:5–23.
   Google Scholar
• Acosta, A. D. (1992). Moderate deviations and associated Laplace approximations for sums of independent random vectors. Trans. Amer. Math. Soc. 329:357–375. DOI: 10.2307/2154092.
   Web of Science ®Google Scholar
• Dembo, A., Zeitouni, O. (1998). Large deviations techniques and applications. In: Applications of Mathematics, vol. 38, 2nd ed. Berlin: Springer-Verlag.
   Google Scholar
• Fatheddin, P. (2015). Central limit theorem for a class of SPDEs. J. Appl. Probab. 52(3):786–796.
   Web of Science ®Google Scholar
• Fatheddin, P., Xiong, J. (2016). Moderate deviation principle for some measure-valued processes. J. Appl. Probab. 53:279–292.
   Google Scholar
• Freidlin, M. I., Wentzell, A. D. (1984). Random Perturbation of Dynamical Systems. Translated by J. Szuc. Berlin: Springer.
   Google Scholar
• Freidlin, M. I. (1988). Random perturbations of reaction-diffusion equations: The quasi-deterministic approach. Trans. Am. Math. Soc. 305:665–697. DOI: 10.2307/2000884.
   Web of Science ®Google Scholar
• Guillin, A. (2003). Averaging principle of SDE with small diffusion: Moderate deviations. Ann. Probab. 31:413–443. DOI: 10.1214/aop/1046294316.
   Web of Science ®Google Scholar
• Hu, Y. (2001). Heat equations with fractional white noise potentials. Appl. Math. Optim. 43(3):221–243. DOI: 10.1007/s00245-001-0001-2.
   Web of Science ®Google Scholar
• Jiang, Y., Shi, K., Wang, Y. (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
• Kolokoltsov, V. (2000). Symmetric stable laws and stable-like jump-diffusions. Proc. London Math. Soc. 80(3):725–768. DOI: 10.1112/S0024611500012314.
   Web of Science ®Google Scholar
• Komatsu, T. (1995). Uniform estimates of fundamental solutions associated with non-local Dirichlet forms. Osaka J. Math. 32:833–860.
   Web of Science ®Google Scholar
• Li, Y., Wang, R., Zhang, S. (2015). Moderate deviations for a stochastic heat equation with spatially correlated noise. Acta Appl. Math. 139(1):59–80. DOI: 10.1007/s10440-014-9969-x.
   Web of Science ®Google Scholar
• Liu, J., Yan, L. (2014). On a semilinear stochastic partial differential equation with double-parameter fractional noises. Sci. China Math. 57(4):855–872. DOI: 10.1007/s11425-013-4703-0.
   Web of Science ®Google Scholar
• Márquez-Carreras, D., Sarrà, M. (2003). Large deviation principle for a stochastic heat equation with spatially corrected noise. Electron. J. Probab. 8(12):1–39.
   Google Scholar
• El Mellali, T., Mellouk, M. (2016). Large deviations for a fractional stocahstic heat equation in spatial dimension Rd driven by a spatially correlated noise. Stoch. Dyn. 16(1):1650001–1650022. DOI: 10.1142/S0219493716500015.
   Google Scholar
• Shi, K. H., Tang, D., Wang, Y. J. (2009). Large deviation principle for stochastic Cahn-Hilliard partial differential equations. Acta Math. Sin-English. Ser. 25(7):1157–1174. DOI: 10.1007/s10114-009-7224-6.
   Web of Science ®Google Scholar
• Sowers, R. (1992). Large deviations for a reaction-diffusion equation with non-Gaussian perturbation. Ann. Probab. 20(1):504–537. DOI: 10.1214/aop/1176989939.
   Web of Science ®Google Scholar
• Truman, A., Wu, J.-L. (2006). On a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws. J. Funct. Anal. 238(2):612–635. DOI: 10.1016/j.jfa.2006.01.012.
   Web of Science ®Google Scholar
• Walsh, J. B. (1986). An introduction to stochastic partial differential equations. In: Ecole D’été de Probabilités de St. Flour XIV, Lect. Notes in Math. Berlin: Springer-Verlag, 1180, pp. 266–439.
   Google Scholar
• Wang, R., Zhang, T. (2015). Moderate deviations for stochastic reaction-diffusion equations with multiplicative noise. Potential Anal. 42(1):99–113. DOI: 10.1007/s11118-014-9425-6.
   Web of Science ®Google Scholar
• Wang, R., Zhai, J., Zhang, T. (2015). A moderate deviation principle for 2-D stochastic Navier-Stokes equations. J. Diff. Eq. 258(10):3363–3390. DOI: 10.1016/j.jde.2015.01.008.
   Web of Science ®Google Scholar
• Yang, J., Jiang, Y. (2016). Moderate deviations for fourth-order stochastic heat equations with fractional noises. Stoch. Dyn. 16(6):1650022. DOI: 10.1142/S0219493716500222.
   Web of Science ®Google Scholar