
Moderate deviations for neutral functional stochastic differential equations driven by Levy noises
Xiaocui MA, Fubao XI, Dezhi LIU
Front. Math. China ›› 2020, Vol. 15 ›› Issue (3) : 529-554.
Moderate deviations for neutral functional stochastic differential equations driven by Levy noises
Using the weak convergence method introduced by A. Budhiraja, P. Dupuis, and A. Ganguly [Ann. Probab., 2016, 44: 1723{1775], we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.
Moderate deviations / neutral functional stochastic dierential equations / Poisson random measure
[1] |
Aldous D. Stopping times and tightness. Ann Probab, 1978, 6: 335–340
CrossRef
Google scholar
|
[2] |
Bao J H, Yuan C G. Large deviations for neutral functional SDEs with jumps. Stochastics, 2015, 87: 48–70
CrossRef
Google scholar
|
[3] |
Budhiraja A, Chen J, Dupuis P. Large deviations for stochastic partial differential equations driven by a Poisson random measure. Stochastic Process Appl, 2013, 123: 523–560
CrossRef
Google scholar
|
[4] |
Budhiraja A, Dupuis P. A variational representation for positive functionals of infinite dimensional Brownian motion. Probab Math Statist, 2000, 20: 39–61
|
[5] |
Budhiraja A, Dupuis P, Ganguly A. Moderate deviation principle for stochastic differential equations with jumps. Ann Probab, 2016, 44: 1723–1775
CrossRef
Google scholar
|
[6] |
Budhiraja A, Dupuis P, Maroulas V. Variational representations for continuous time processes. Ann Inst Henri Poincaré Probab Stat, 2011, 47: 725–747
CrossRef
Google scholar
|
[7] |
Cai Y J, Huang J H, Maroulas V. Large deviations of mean-field stochastic differential equations with jumps. Statist Probab Lett, 2015, 96: 1–9
CrossRef
Google scholar
|
[8] |
Cerrai S, Röckner M. Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Ann Probab, 2004, 32: 1100–1139
CrossRef
Google scholar
|
[9] |
Dembo A, Zeitouni O, Large Deviations Techniques and Applications. San Diego: Academic Press, 1989
|
[10] |
Dong Z, Xiong J, Zhai J L, Zhang T. A moderate deviation principle for 2-D stochastic Navier-Stokes equations driven by multiplicative Levy noises. J Funct Anal, 2017, 272: 227–254
CrossRef
Google scholar
|
[11] |
Dunford N, Schwartz J. Linear Operators, Part I. New York: Wiley, 1988
|
[12] |
Dupuis P, Ellis R S. A Weak Convergence Approach to the Theory of Large Deviations. New York: Wiley, 1997
CrossRef
Google scholar
|
[13] |
Freidlin M I. Random perturbations of reaction-diffusion equations: the quasideterministic approach. Trans Amer Math Soc, 1988, 305: 665–697
CrossRef
Google scholar
|
[14] |
Freidlin M I, Wentzell A D. Random Perturbations of Dynamical Systems. New York: Springer, 1984
CrossRef
Google scholar
|
[15] |
Guillin A. Averaging principle of SDE with small diffusion: moderate deviations. Ann Probab, 2003, 31: 413–443
CrossRef
Google scholar
|
[16] |
Guillin A, Liptser R. Examples of moderate deviation principle for diffusion processes. Discrete Contin Dyn Syst Ser B, 2006, 6: 803–828
CrossRef
Google scholar
|
[17] |
He Q, Yin G. Large deviations for multi-scale Markovian switching systems with a small diffusion. Asymptot Anal, 2014, 87: 123–145
CrossRef
Google scholar
|
[18] |
He Q, Yin G. Moderate deviations for time-varying dynamic systems driven by nonhomogeneous Markov chains with two-time scales. Stochastics, 2014, 86: 527–550
CrossRef
Google scholar
|
[19] |
He Q, Yin G, Zhang Q. Large deviations for two-time-scale systems driven by nonhomogeneous Markov chains and associated optimal control problems. SIAM J Control Optim, 2011, 49: 1737–1765
CrossRef
Google scholar
|
[20] |
Kallianpur G, Xiong J. Large deviations for a class of stochastic partial differential equations. Ann Probab, 1996, 24: 320–345
CrossRef
Google scholar
|
[21] |
Ma X C, Xi F B. Moderate deviations for neutral stochastic differential delay equations with jumps. Statist Probab Lett, 2017, 126: 97–107
CrossRef
Google scholar
|
[22] |
Mao X. Stochastic Differential Equations and Applications. Amsterdam: Elsevier, 2007
CrossRef
Google scholar
|
[23] |
Maroulas V. Uniform large deviations for infinite dimensional stochastic systems with jumps. Mathematika, 2011, 57: 175–192
CrossRef
Google scholar
|
[24] |
Peszat S. Large derivation principle for stochastic evolution equations. Probab Theory Related Fields, 1994, 98: 113–136
CrossRef
Google scholar
|
[25] |
Röckner M, Zhang T, Zhang X. Large deviations for stochastic tamed 3D Navier-Stokes equations. Appl Math Optim, 2010, 61: 267–285
CrossRef
Google scholar
|
[26] |
Sowers R. Large deviations for a reaction-diffusion equation with non-Gaussian perturbations. Ann Probab, 1992, 20: 504–537
CrossRef
Google scholar
|
[27] |
Suo Y Q, Tao J, Zhang W. Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth. Front Math China, 2018, 13: 913–933
CrossRef
Google scholar
|
[28] |
Wang R, Zhai J L, Zhang T. A moderate deviation principle for 2-D stochastic Navier-Stokes equations. J Differential Equations, 2015, 258: 3363–3390
CrossRef
Google scholar
|
[29] |
Wang R, Zhang T. Moderate deviations for stochastic reaction-diffusion equations with multiplicative noise. Potential Anal, 2015, 42: 99–113
CrossRef
Google scholar
|
[30] |
Zhai J L, Zhang T. Large deviations for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises. Bernoulli, 2015, 21: 2351{2392
CrossRef
Google scholar
|
[31] |
Zhang X. Euler schemes and large deviations for stochastic Volterra equations with singular kernels. J Differential Equations, 2008, 244: 2226–2250
CrossRef
Google scholar
|
/
〈 |
|
〉 |