Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 1, p. 69-105
@article{AIHPB_2005__41_1_69_0,
     author = {Cerrai, Sandra and R\"ockner, Michael},
     title = {Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {41},
     number = {1},
     year = {2005},
     pages = {69-105},
     doi = {10.1016/j.anihpb.2004.03.001},
     zbl = {1066.60029},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2005__41_1_69_0}
}
Cerrai, Sandra; Röckner, Michael. Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 1, pp. 69-105. doi : 10.1016/j.anihpb.2004.03.001. http://www.numdam.org/item/AIHPB_2005__41_1_69_0/

[1] S. Cerrai, Second Order PDE's in Finite and Infinite Dimension. A Probabilistic Approach, Lecture Notes in Mathematics, vol. 1762, Springer-Verlag, Berlin, 2001. | MR 1840644 | Zbl 0983.60004

[2] S. Cerrai, Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Probab. Theory Related Fields 125 (2003) 271-304. | MR 1961346 | Zbl 1027.60064

[3] S. Cerrai, M. Röckner, Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Ann. Probab. 32 (2004) 1-40. | MR 2044675 | Zbl 1054.60065

[4] Ph. Clément, G. Sweers, Uniform anti-maximum principles, J. Differential Equations 164 (2000) 118-154. | MR 1761420 | Zbl 0964.35033

[5] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1989. | MR 990239 | Zbl 0699.35006

[6] I. Daw, Principe de grandes déviationes pour une mesure invariante associée à un processus de diffusion en dimension infinie, Ph.D. Thesis, University of Rouen (1998).

[7] M.D. Donsker, S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, Comm. Pure Appl. Math. 28 (1975) 1-47. | MR 386024 | Zbl 0323.60069

[8] W.G. Faris, G. Jona-Lasinio, Large fluctuation for a non linear heat equation with noise, J. Phys. A 15 (1982) 3025-3055. | MR 684578 | Zbl 0496.60060

[9] M.I. Freidlin, Random perturbations of reaction-diffusion equations: the quasi deterministic approximation, Trans. Amer. Math. Soc. 305 (1988) 665-697. | MR 924775 | Zbl 0673.35049

[10] M.I. Freidlin, A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag, Berlin, 1984. | MR 722136 | Zbl 0922.60006

[11] S. Peszat, Large deviation estimates for stochastic evolution equations, Probab. Theory Related Fields 98 (1994) 113-136. | MR 1254827 | Zbl 0792.60057

[12] T. Runst, W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators and Nonlinear Partial Differential Equations, Walter de Gruyter, Berlin, 1996. | MR 1419319 | Zbl 0873.35001

[13] R. Sowers, Large deviations for a reaction-diffusion equation with non-Gaussian perturbation, Ann. Probab. 20 (1992) 504-537. | MR 1143433 | Zbl 0749.60059

[14] R. Sowers, Large deviations for the invariant measure of a reaction-diffusion equation with non-Gaussian perturbations, Probab. Theory Related Fields 92 (1992) 393-421. | MR 1165518 | Zbl 0767.60025

[15] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. | MR 503903 | Zbl 0387.46032

[16] S.R.S. Varadhan, Asymptotic probabilities and differential equations, Comm. Pure Appl. Math. 22 (1969) 261-286. | MR 203230 | Zbl 0147.15503