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References

  • Florent Barret, Sharp asymptotics of metastable transition times for one dimensional SPDEs, arXiv:1201.4440, 2012.
  • Barret, Florent; Bovier, Anton; Méléard, Sylvie. Uniform estimates for metastable transition times in a coupled bistable system. Electron. J. Probab. 15 (2010), no. 12, 323-345. MR2609590
  • Nils Berglund, Kramers' law: Validity, derivations and generalisations, arXiv:1106.5799v1, 2011.
  • Berglund, Nils; Fernandez, Bastien; Gentz, Barbara. Metastability in interacting nonlinear stochastic differential equations. I. From weak coupling to synchronization. Nonlinearity 20 (2007), no. 11, 2551-2581. MR2361246
  • Berglund, Nils; Fernandez, Bastien; Gentz, Barbara. Metastability in interacting nonlinear stochastic differential equations. II. Large-$N$ behaviour. Nonlinearity 20 (2007), no. 11, 2583-2614. MR2361247
  • Berglund, Nils; Gentz, Barbara. Anomalous behavior of the Kramers rate at bifurcations in classical field theories. J. Phys. A 42 (2009), no. 5, 052001, 9 pp. MR2525368
  • Nils Berglund and Barbara Gentz, The Eyring-Kramers law for potentials with nonquadratic saddles, Markov Processes Relat. Fields 16 (2010), 549-598. MR2759772 (2011i:60139)
  • Dirk Blömker and Arnulf Jentzen, Galerkin approximations for the stochastic Burgers equation, to appear in SIAM J. Numer. Anal., 2013.
  • Bovier, Anton; Eckhoff, Michael; Gayrard, Véronique; Klein, Markus. Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times. J. Eur. Math. Soc. (JEMS) 6 (2004), no. 4, 399-424. MR2094397
  • Bovier, Anton; Gayrard, Véronique; Klein, Markus. Metastability in reversible diffusion processes. II. Precise asymptotics for small eigenvalues. J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 69-99. MR2120991
  • Cerrai, Sandra. Elliptic and parabolic equations in ${\bf R}^ n$ with coefficients having polynomial growth. Comm. Partial Differential Equations 21 (1996), no. 1-2, 281-317. MR1373775
  • Cerrai, Sandra. Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces. Probab. Theory Related Fields 113 (1999), no. 1, 85-114. MR1670729
  • Chafee, N.; Infante, E. F. A bifurcation problem for a nonlinear partial differential equation of parabolic type. Applicable Anal. 4 (1974/75), 17-37. MR0440205
  • Chenal, Fabien; Millet, Annie. Uniform large deviations for parabolic SPDEs and applications. Stochastic Process. Appl. 72 (1997), no. 2, 161-186. MR1486551
  • Colin de Verdière, Yves. Déterminants et intégrales de Fresnel. (French) [Determinants and Fresnel integrals] Symposium à la Mémoire de François Jaeger (Grenoble, 1998). Ann. Inst. Fourier (Grenoble) 49 (1999), no. 3, 861-881. MR1703428
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • den Hollander, F. Metastability under stochastic dynamics. Stochastic Process. Appl. 114 (2004), no. 1, 1-26. MR2094145
  • Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons Inc., New York, 1988. MR1009162 (90g:47001a)
  • H. Eyring, The activated complex in chemical reactions, Journal of Chemical Physics 3 (1935), 107-115.
  • Faris, William G.; Jona-Lasinio, Giovanni. Large fluctuations for a nonlinear heat equation with noise. J. Phys. A 15 (1982), no. 10, 3025-3055. MR0684578
  • Forman, Robin. Functional determinants and geometry. Invent. Math. 88 (1987), no. 3, 447-493. MR0884797
  • Freidlin, M. I.; Wentzell, A. D. Random perturbations of dynamical systems. Translated from the 1979 Russian original by Joseph Szücs. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 260. Springer-Verlag, New York, 1998. xii+430 pp. ISBN: 0-387-98362-7 MR1652127
  • Freidlin, Mark I. Random perturbations of reaction-diffusion equations: the quasideterministic approximation. Trans. Amer. Math. Soc. 305 (1988), no. 2, 665-697. MR0924775
  • Gallay, Th. A center-stable manifold theorem for differential equations in Banach spaces. Comm. Math. Phys. 152 (1993), no. 2, 249-268. MR1210168
  • Hairer, Martin. An introduction to stochastic PDEs. Lecture notes, 2009. http://arxiv.org/abs/0907.4178
  • Jetschke, G. On the equivalence of different approaches to stochastic partial differential equations. Math. Nachr. 128 (1986), 315-329. MR0855965
  • Jolly, Michael S. Explicit construction of an inertial manifold for a reaction diffusion equation. J. Differential Equations 78 (1989), no. 2, 220-261. MR0992147
  • Kramers, H. A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, (1940). 284-304. MR0002962
  • Liu, Di. Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise. Commun. Math. Sci. 1 (2003), no. 2, 361-375. MR1980481
  • Robert S. Maier and D. L. Stein, Droplet nucleation and domain wall motion in a bounded interval, Phys. Rev. Lett. 87 (2001), 270601-1.
  • Robert S. Maier and D. L. Stein, The effects of weak spatiotemporal noise on a bistable one-dimensional system, Noise in complex systems and stochastic dynamics (L. Schimanski-Geier, D. Abbott, A. Neimann, and C. Van den Broeck, eds.), SPIE Proceedings Series, vol. 5114, 2003, pp. 67-78.
  • Martinelli, Fabio; Olivieri, Enzo; Scoppola, Elisabetta. Small random perturbations of finite- and infinite-dimensional dynamical systems: unpredictability of exit times. J. Statist. Phys. 55 (1989), no. 3-4, 477-504. MR1003525
  • McKane, Alan J.; Tarlie, Martin B. Regularization of functional determinants using boundary perturbations. J. Phys. A 28 (1995), no. 23, 6931-6942. MR1381151
  • Olivieri, Enzo; Vares, Maria Eulália. Large deviations and metastability. Encyclopedia of Mathematics and its Applications, 100. Cambridge University Press, Cambridge, 2005. xvi+512 pp. ISBN: 0-521-59163-5 MR2123364
  • Saitoh, Saburou. Weighted $L_ p$-norm inequalities in convolutions. Survey on classical inequalities, 225--234, Math. Appl., 517, Kluwer Acad. Publ., Dordrecht, 2000. MR1894722
  • D. L. Stein, Critical behavior of the Kramers escape rate in asymmetric classical field theories, J. Stat. Phys. 114 (2004), 1537-1556.
  • D. L. Stein, Large fluctuations, classical activation, quantum tunneling, and phase transitions, Braz. J. Phys. 35 (2005), 242-252.
  • Ventcelʹ, A. D.; Freĭdlin, M. I. Small random perturbations of a dynamical system with stable equilibrium position. (Russian) Dokl. Akad. Nauk SSSR 187 1969 506-509. MR0249795
  • Vinokurov, V. A.; Sadovnichiĭ, V. A. Asymptotics of arbitrary order of the eigenvalues and eigenfunctions of the Sturm-Liouville boundary value problem in an interval with a summable potential. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), no. 4, 47-108; translation in Izv. Math. 64 (2000), no. 4, 695-754 MR1794595


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