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Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions
Large deviations for neutral stochastic functional differential equations
Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, UK |
In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) an exponential approximation argument to investigate large deviations for neutral stochastic functional differential equations.
References:
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J. Bao, G. Yin and C. Yuan, Asymptotic Analysis for Functional Stochastic Differential Equations, Springer, Cham, 2016.
doi: 10.1007/978-3-319-46979-9. |
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J. Bao and C. Yuan,
Large deviations for neutral functional SDEs with jumps, Stochastic, 87 (2015), 48-70.
doi: 10.1080/17442508.2014.914516. |
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Li. Bo and T. Zhang,
Large deviations for perturbed reflected diffusion processes, Stochastics, 81 (2009), 531-543.
doi: 10.1080/17442500801981084. |
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A. Budhiraja, J. Chen and P. Dupuis,
Large deviations for stochastic partial differential equations driven by Poisson random measure, Stochastic Process. Appl., 123 (2013), 523-560.
doi: 10.1016/j.spa.2012.09.010. |
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A. Budhiraja, P. Dupuis and M. Fischer,
Large deviation properties of weakly interacting processes via weak convergence methods, Ann. Probab., 40 (2012), 74-102.
doi: 10.1214/10-AOP616. |
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A. Budhiraja, P. Dupuis and A. Ganguly,
Large deviations for small noise diffusions in a fast Markovian environment, Election. J. Probab., 23 (2018), 1-33.
doi: 10.1214/18-EJP228. |
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A. Budhiraja and P. Nyquist,
Large deviations for multidimensional state-dependent shot-noise processes, J. Appl. Probab., 52 (2015), 1097-1114.
doi: 10.1239/jap/1450802755. |
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A. Dembo and A. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, Berlin Heidelberg, 1998.
doi: 10.1007/978-1-4612-5320-4. |
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M. Freidlin,
Random perturbations of reaction-diffusion equations: the quasi-deterministic approximation, Trans. Amer. Math. Soc., 305 (1988), 665-697.
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S. Gadat, F. Panloup and C. Pellegrini, Large deviation principle for invariant distributions of memory gradient diffusions, Electron. J. Probab., 18 (2013), 34pp.
doi: 10.1214/EJP.v18-2031. |
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G. Huang, M. Mandjes and P. Spreij,
Large deviations for Markov-modulated diffusion processes with rapid switching, Stochastic Process. Appl., 126 (2016), 1785-1818.
doi: 10.1016/j.spa.2015.12.005. |
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R. S. Liptser and A. A. Pukhalskii,
Limit theorems on large deviations for semimartingales, Stochastics Stochastics Rep., 38 (1992), 201-249.
doi: 10.1080/17442509208833757. |
| [13] |
K. Liu and T. Zhang,
A large deviation principle of retarded Ornstein-Uhlenbeck processes driven by Levy noise, Stoch. Anal. Appl., 32 (2014), 889-910.
doi: 10.1080/07362994.2014.939544. |
| [14] |
X. Mao, Stochastic Differential Equations and Applications, 2$^{nd}$ edition, Horwood Publishing Limited, Chichester, 2008.
doi: 10.1533/9780857099402. |
| [15] |
C. Mo and J. Luo,
Large deviations for stochastic differential delay equations, Nonlinear Anal., 80 (2013), 202-210.
doi: 10.1016/j.na.2012.10.004. |
| [16] |
S. A. Mohammed and T. Zhang, Large deviations for stochastic systems with memory, Discrete Contin. Dyn. Syst. Ser. B, 66 (2006), 881–893.
doi: 10.3934/dcdsb.2006.6.881. |
| [17] |
M. Röckner and T. Zhang,
Stochastic evolution equations of jump type: existence, uniqueness and large deviation principles, Potential Anal., 26 (2007), 255-279.
doi: 10.1007/s11118-006-9035-z. |
| [18] |
D.W. Stroock, An Introduction to the Theory of Large Deviations, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-1-4613-8514-1. |
| [19] |
Y. Suo, J. Tao and W. Zhang,
Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth, Front. Math. China, 13 (2018), 913-933.
doi: 10.1007/s11464-018-0710-3. |
show all references
References:
| [1] |
J. Bao, G. Yin and C. Yuan, Asymptotic Analysis for Functional Stochastic Differential Equations, Springer, Cham, 2016.
doi: 10.1007/978-3-319-46979-9. |
| [2] |
J. Bao and C. Yuan,
Large deviations for neutral functional SDEs with jumps, Stochastic, 87 (2015), 48-70.
doi: 10.1080/17442508.2014.914516. |
| [3] |
Li. Bo and T. Zhang,
Large deviations for perturbed reflected diffusion processes, Stochastics, 81 (2009), 531-543.
doi: 10.1080/17442500801981084. |
| [4] |
A. Budhiraja, J. Chen and P. Dupuis,
Large deviations for stochastic partial differential equations driven by Poisson random measure, Stochastic Process. Appl., 123 (2013), 523-560.
doi: 10.1016/j.spa.2012.09.010. |
| [5] |
A. Budhiraja, P. Dupuis and M. Fischer,
Large deviation properties of weakly interacting processes via weak convergence methods, Ann. Probab., 40 (2012), 74-102.
doi: 10.1214/10-AOP616. |
| [6] |
A. Budhiraja, P. Dupuis and A. Ganguly,
Large deviations for small noise diffusions in a fast Markovian environment, Election. J. Probab., 23 (2018), 1-33.
doi: 10.1214/18-EJP228. |
| [7] |
A. Budhiraja and P. Nyquist,
Large deviations for multidimensional state-dependent shot-noise processes, J. Appl. Probab., 52 (2015), 1097-1114.
doi: 10.1239/jap/1450802755. |
| [8] |
A. Dembo and A. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, Berlin Heidelberg, 1998.
doi: 10.1007/978-1-4612-5320-4. |
| [9] |
M. Freidlin,
Random perturbations of reaction-diffusion equations: the quasi-deterministic approximation, Trans. Amer. Math. Soc., 305 (1988), 665-697.
doi: 10.2307/2000884. |
| [10] |
S. Gadat, F. Panloup and C. Pellegrini, Large deviation principle for invariant distributions of memory gradient diffusions, Electron. J. Probab., 18 (2013), 34pp.
doi: 10.1214/EJP.v18-2031. |
| [11] |
G. Huang, M. Mandjes and P. Spreij,
Large deviations for Markov-modulated diffusion processes with rapid switching, Stochastic Process. Appl., 126 (2016), 1785-1818.
doi: 10.1016/j.spa.2015.12.005. |
| [12] |
R. S. Liptser and A. A. Pukhalskii,
Limit theorems on large deviations for semimartingales, Stochastics Stochastics Rep., 38 (1992), 201-249.
doi: 10.1080/17442509208833757. |
| [13] |
K. Liu and T. Zhang,
A large deviation principle of retarded Ornstein-Uhlenbeck processes driven by Levy noise, Stoch. Anal. Appl., 32 (2014), 889-910.
doi: 10.1080/07362994.2014.939544. |
| [14] |
X. Mao, Stochastic Differential Equations and Applications, 2$^{nd}$ edition, Horwood Publishing Limited, Chichester, 2008.
doi: 10.1533/9780857099402. |
| [15] |
C. Mo and J. Luo,
Large deviations for stochastic differential delay equations, Nonlinear Anal., 80 (2013), 202-210.
doi: 10.1016/j.na.2012.10.004. |
| [16] |
S. A. Mohammed and T. Zhang, Large deviations for stochastic systems with memory, Discrete Contin. Dyn. Syst. Ser. B, 66 (2006), 881–893.
doi: 10.3934/dcdsb.2006.6.881. |
| [17] |
M. Röckner and T. Zhang,
Stochastic evolution equations of jump type: existence, uniqueness and large deviation principles, Potential Anal., 26 (2007), 255-279.
doi: 10.1007/s11118-006-9035-z. |
| [18] |
D.W. Stroock, An Introduction to the Theory of Large Deviations, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-1-4613-8514-1. |
| [19] |
Y. Suo, J. Tao and W. Zhang,
Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth, Front. Math. China, 13 (2018), 913-933.
doi: 10.1007/s11464-018-0710-3. |
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