Open Access
Volume 27, 2023
Page(s) 558 - 575
Published online 28 April 2023
  1. A. Budhiraja, J. Chen and P. Dupuis, Large deviations for stochastic partial differential equations driven by a Poisson random measure. Stochastic Process Appl. 123 (2013) 523–560. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion. Probab. Math. Stat. 20 (2000) 39–61. [Google Scholar]
  3. A. Budhiraja, P. Dupuis and V. Maroulas, Large deviations for infinite dimensional stochastic dynamical systems. Ann. Probab. 36 (2008) 1390–1420. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Bao and C. Yuan, Large deviations for neutral functional SDEs with jumps. Stochastics 87 (2015) 48–70. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Boué and P. Dupuis, A variational representation for certain functionals of Brownian motion. Ann. Probab. 26 (1998) 1641–1659. [MathSciNet] [Google Scholar]
  6. M. Boue, P. Dupuis and R.S. Ellis, Large deviations for small noise diffusions with discontinuous statistics. Probab. Theory Related Fields 116 (2000) 125–149. [CrossRef] [MathSciNet] [Google Scholar]
  7. P.L. Chow, Some parabolic Itô equations. Commun. Pure Appl. Math. 45 (1992) 97–120. [CrossRef] [Google Scholar]
  8. E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955). [Google Scholar]
  9. P. Dupuis and R.S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York (1997). [CrossRef] [Google Scholar]
  10. M.I. Freidlin and A.D. Wentzell, On small random perturbations of dynamical system. Russian Math. Surveys 25 (1970) 1–55. [Google Scholar]
  11. G. Kallianpur and J. Xiong, Stochastic differential equations in infinite dimensional spaces. IMS Lecture Notes- Monograph Series, vol. 26. Institute Math. Stat. (1995). [Google Scholar]
  12. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. Graduate Texts in Mathematics. Springer- Verlag, New York (1991). [Google Scholar]
  13. A. Kolmogorov and S. Fomin, Elements of the Theory of Functions and Functional Analysis. Graylock, Rochester (1957). [Google Scholar]
  14. Y. Ma, R. Wang and L. Wu, Moderate Deviation Principle for dynamical systems with small random perturbation. J. Math. 32 (2012) 395–401. [Google Scholar]
  15. V. Maroulas, Large deviations for infinite-dimensional stochastic systems with jumps. Mathematika 57 (2011) 175–192. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. Ren, Large deviation principle for homeomorphism flows of stochastic Hamiltonian systems. Acta Math. Sin. (Chin. Ser.) 61 (2018) 383–402. [Google Scholar]
  17. J. Ren and X. Zhang, Freidlin-Wentzell’s large deviations for stochastic evolution equations. J. Funct. Anal. 254 (2008) 3148–3172. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Ren and X. Zhang, Freidlin-Wentzell’s large deviations for homemorphism flows of non-Lipschitz SDEs. Bull. Sci. Math. 129 (2005) 643–655. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Ren and X. Zhang, Schilder theorem for the Brownian motion on the diffeomorphism group of the circle. J. Funct. Anal. 224 (2005) 107–133. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Sowers, Large deviations for a reaction diffusion equation with non-Gaussian perturbations. Ann. Probab. 20 (1992) 504–537. [CrossRef] [MathSciNet] [Google Scholar]
  21. Y. Suo, J. Tao and W. Zhang, Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth. Front. Math. China 013 (2018) 913–933. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Wang, J. Zhai and T. Zhang, A moderate deviation principle for 2-D stochastic Navier-Stokes equations. J. Differ. Equ. 258 (2015) 3363–3390. [CrossRef] [Google Scholar]
  23. R. Wang and T. Zhang, Moderate deviations for stochastic reaction-diffusion equations with multiplicative noise. Potential Anal. 42 (2015) 99–113. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Wu, Uniform large deviations for multivalued stochastic differential equations with Poisson jumps. Kyoto J Math. 51 (2011) 535–559. [MathSciNet] [Google Scholar]
  25. L. Wu, Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems. Stochastic Process. Appl. 91 (2001) 205–238. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Xie and X. Zhang, Ergodicity of stochastic differential equations with jumps and singular coefficients. Ann. I. H. Poincare 56 (2020) 175–229. [Google Scholar]
  27. T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 (1971) 155–167. [MathSciNet] [Google Scholar]
  28. F. X. C. Zhou and F. Wu, On strong Feller property, exponential ergodicity and large deviations principle for stochastic damping Hamiltonian systems with state-dependent switching. J. Differ. Equ. 286 (2021) 856–891. [CrossRef] [Google Scholar]
  29. X. Zhang, Stochastic flows and Bismut formulas for stochastic Hamiltonian systems. Stochastic Process Appl. 120 (2010) 1929–1949. [CrossRef] [MathSciNet] [Google Scholar]
  30. X. Zhang, Stochastic Volterra equations in Banach spaces and stochastic partial differential equation. J. Funct. Anal. 258 (2010) 1361–1425. [CrossRef] [MathSciNet] [Google Scholar]
  31. X. Zhang, Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. Rev. Mat. Iberoamericana 29 (2013) 25–52. [CrossRef] [MathSciNet] [Google Scholar]
  32. X. Zhang, A variational representation for random functionals on abstract Wiener spaces. J. Math. Kyoto Univ. 49 (2009) 475–490. [MathSciNet] [Google Scholar]

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