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Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations with Poisson Jumps

DOI: 10.4236/apm.2016.610056, PP. 676-694

Keywords: Stochastic Evolution Equation, Poisson Jumps, Freidlin-Wentzell’s Large Deviation, Weak Convergence Method

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Abstract:

We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.

References

[1]  Dupuis, P. and Ellis, R.S. (1997) A Weak Convergence Approach to the Theory of Large Deviations. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley and Sons, Inc., New York.
http://dx.doi.org/10.1002/9781118165904
[2]  Boué, M. and Dupuis, P. (1998) A Variational Representation for Certain Functionals of Brownian Motion. Annals of Probability, 26, 1641-1659.
[3]  Zhang, X. (2009) A Variational Representation for Random Funcionals on Abstract Wiener Spaces. Journal of Mathematics of Kyoto University, 49, 475-490.
[4]  Zhang, X. (2009) Clark-Ocone Formula and Variational Representation for Poisson Functionals. Annals of Probability, 37, 506-529.
http://dx.doi.org/10.1214/08-AOP411
[5]  Budhiraja, A., Dupuis, P. and Maroulas, V. (2011) Variational Representations for Continuous Time Process. Annales de l Institut Henri Poincaré Probabilités et Statistiques, 47, 725-747.
[6]  Boué, M., Dupuis, P. and Ellis, R.S. (2000) Large Deviations for Small Noise Diffusions with Discontinuous Statistics. Probability Theory and Related Fields, 116, 125-149.
http://dx.doi.org/10.1007/PL00008720
[7]  Budhiraja, A., Dupuis, P. and Maroulas, V. (2008) Large Deviations for Infinite Dimensional Stochastic Dynamical Systems. Annals of Probability, 36, 1390-1420.
http://dx.doi.org/10.1214/07-AOP362
[8]  Liu, W. (2010) Large Deviation for Stochastic Evolution Equations with Small Multiplicative Noise. Applied Mathematics & Optimization, 61, 27-56.
http://dx.doi.org/10.1007/s00245-009-9072-2
[9]  Ren, J. and Zhang, X. (2008) Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations. Journal of Functional Analysis, 254, 3148-3172.
http://dx.doi.org/10.1016/j.jfa.2008.02.010
[10]  Zhang, X. (2008) Euler Schemes and Large Deviations for Stochastic Volterra Equations with Singular Kernels. Journal of Differential Equations, 224, 2226-2250.
http://dx.doi.org/10.1016/j.jde.2008.02.019
[11]  Röckner, M. and Zhang, T. (2007) Stochastic Evolution Equations of Jump Type: Existence, Uniqueness and Large Deviation Principles. Potential Analysis, 26, 255-279.
http://dx.doi.org/10.1007/s11118-006-9035-z
[12]  Budhiraja, A., Chen, J. and Dupuis, P. (2013) Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure. Stochastic Processes and their Applications, 123, 523-560.
http://dx.doi.org/10.1016/j.spa.2012.09.010
[13]  Gyöngy, I. and Krylov, N.V. (1980) On Stochastic Equations with Respect to Semimartingales I. Stochastics, 4, 1-21.
http://dx.doi.org/10.1080/03610918008833154
[14]  Gyöngy, I. and Krylov, N.V. (1982) On Stochastic Equations with Respect to Semimartingales II, Ito Formula in Banach Spaces. Stochastics, 6, 153-174.
http://dx.doi.org/10.1080/17442508208833202
[15]  Gyöngy, I. (1982) On Stochastic Equations with Respect to Semimartingales III. Stochastics, 7, 231-254.
http://dx.doi.org/10.1080/17442508208833220
[16]  Ren, J., Röckner, M. and Wang, F. (2007) Stochastic Generalixed Porous Media and fast Diffusion Equation. Journal of Differential Equations, 238, 118-152.
http://dx.doi.org/10.1016/j.jde.2007.03.027
[17]  Zhao, H. (2009) On Existence and Uniqueness of Stochastic Evolution Equation with Poisson Jumps. Statistics & Probability Letters, 79, 2367-2373.
http://dx.doi.org/10.1016/j.spl.2009.08.006
[18]  Yang, X., Zhai, J. and Zhang, T. (2015) Large Deviations for SPDEs of Jump Type. Stochastic and Dynamics, 15.
[19]  Dadashi, H. (2013) Large Deviation Principle for Mild Solutions of Stochastic Evolution Equations with Multiplicative Lévy Noise. arXiv:1309.1935v1 [math.PR]
http://arxiv.org/pdf/1309.1935.pdf
[20]  Jacod, J. and Shiryaev, A. (1980) Limit Theorems for Stochastic Processes. Springer-Verlag, New York.
[21]  Kallenberg, O. (2002) Foudations of Modern Probability. 2nd Edition, Applied Probability Trust.
http://dx.doi.org/10.1007/978-1-4757-4015-8

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