References
- J. Bao and C. Yuan, Large deviations for neutral functional SDEs with jumps, Stochastics 87 (2015), pp. 48–70. doi: 10.1080/17442508.2014.914516
- A. Budhiraja, J. Chen, and P. Dupuis, Large deviations for stochastic partial differential equations driven by a Poisson random measure, Stoch. Process. Appl. 123 (2013), pp. 523–560. doi: 10.1016/j.spa.2012.09.010
- A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion, Probab. Math. Statist. 20 (2000), pp. 39–61.
- A. Budhiraja, P. Dupuis, and A. Ganguly, Moderate deviation principles for stochastic differential equations with jumps, Ann. Probab. 44 (2016), pp. 1723–1775. doi: 10.1214/15-AOP1007
- A. Budhiraja, P. Dupuis, and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. H. Poincaré 47 (2011), pp. 725–747. doi: 10.1214/10-AIHP382
- Y. Cai, J. Huang, and V. Maroulas, Large deviations of mean-field stochastic differential equations with jumps, Stat. Probab. Lett. 96 (2015), pp. 1–9. doi: 10.1016/j.spl.2014.08.010
- S. Cerrai and M. Röckner, Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Ann. Inst. H. Poincaré, 41 (2005), pp. 69–105. doi: 10.1016/j.anihpb.2004.03.001
- A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Academic Press, San Diego, CA, 1989.
- Z. Dong and Y. Xie, Ergodicity of linear SPDE driven by Lévy noise, J. Syst. Sci. Complex. 23 (2010), pp. 137–152. doi: 10.1007/s11424-010-9269-0
- Z. Dong and Y. Xie, Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise, J. Differential Equations 251 (2011), pp. 196–222. doi: 10.1016/j.jde.2011.03.015
- P. Dupuis and R. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, Wiley, New York, 1997.
- M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer, New York, 1984.
- I.I. Gihmann and A.V. Skorohod, Stochastic Differential Equations, Springer, Berlin, Heidelberg, New York, 1972.
- Y. Kwon and C. Lee, Strong feller property and irreducibility of diffusions with jumps, Kwon Y, Ff C I. Strong feller property and irreducibility of diffusions with jumps, Stochastics, 67(1–2) (1999), pp. 147–157.
- V. Maroulas, Uniform large deviations for infinite dimensional stochastic systems with jumps, Mathematika 57 (2011), pp. 175–192. doi: 10.1112/S0025579310001282
- S. Peszat and J. Zabczyk, Strong feller property and irreducibility of diffusions on Hilbert spaces, Ann. Probab. 23 (1995), pp. 157–172. doi: 10.1214/aop/1176988381
- D. Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press, Cambridge, 1996.
- R. Situ, Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering, Springer, New York, 2005.
- R. Sowers, Large deviations for the invariant measures of a reaction-diffusion equation with non-Gaussian perturbations, Probab. Theory Relat. 92 (1992), pp. 393–421. doi: 10.1007/BF01300562
- S.R.S. Varadhan, Large Deviations and Applications, SIAM, Philadelphia, 1984.
- J. Wu, Uniform large deviations for multivalued stochastic differential equations with Poisson jumps, Kyoto J. Math. 51 (2011), pp. 535–559. doi: 10.1215/21562261-1299891
- F. Xi, Invariant measures for a random evolution equation with small perturbations, Acta Math. Sin. 17 (2001), pp. 631–642. doi: 10.1007/s101140100127
- F. Xi, Invariant measure for the Markov process corresponding to a PDE system, Acta Math. Sin. 21 (2005), pp. 457–464. doi: 10.1007/s10114-004-0510-4
- F. Xi and G. Yin, Almost sure stability and instability for switching-jump-diffusion systems with state-dependent switching, J. Math. Anal. Appl. 400 (2013), pp. 460–474. doi: 10.1016/j.jmaa.2012.10.062
- X. Yang, J. Zhai and T. Zhang, Large deviations for SPDEs of jump type, Stoch. Dyn. 15 (2015), p. 1550026. doi: 10.1142/S0219493715500264
- G. Yin and C. Zhu, Properties of solutions of stochastic differential equations with continuous-state-dependent switching, J. Differential Equations 249 (2010), pp. 2409–2439. doi: 10.1016/j.jde.2010.08.008
- J. Zhai and T. Zhang, Large deviations for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises, Bernoulli 21 (2015), pp. 2351–2392. doi: 10.3150/14-BEJ647
- T. Zhang, Large deviations for invariant measures of SPDEs with two reflecting walls, Stoch. Process Appl. 122 (2012), pp. 3425–3444. doi: 10.1016/j.spa.2012.06.003
- X. Zhang, Exponential ergodicity of non-Lipschitz stochastic differential equations, Proc. Am. Math. Soc. 137 (2009), pp. 329–337. doi: 10.1090/S0002-9939-08-09509-9