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References

  • Bell, D.R. and Mohammed, S.E.A.: An extension of H\"ormander's theorem for infinitely degenerate second-order operators. Duke Math. J. 78 (1995), no. 3, 453--475. MR1334203
  • Cattiaux, P., Leon, J.R. and Prieur, C.: Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. phI. Invariant density[J], (2012).
  • Cinti, C., Menozzi, S and Polidoro, S.: Two-sided bounds for degenerate processes with densities supported in subsets of mathbbR^ N. pharXiv:1203.4918, (2012).
  • Da Prato, G. and Zabczyk, J.: Ergodicity for infinite-dimensional systems. London Mathematical Society Lecture Note Series, 229. Cambridge University Press, Cambridge, 1996. xii+339 pp. ISBN: 0-521-57900-7 MR1417491
  • Delarue, F. and Menozzi, S.: Density estimates for a random noise propagating through a chain of differential equations. J. Funct. Anal. 259 (2010), no. 6, 1577--1630. MR2659772
  • Flandoli, Franco.: Dissipativity and invariant measures for stochastic Navier-Stokes equations. NoDEA Nonlinear Differential Equations Appl. 1 (1994), no. 4, 403--423. MR1300150
  • Flandoli, Franco. and Maslowski, Bohdan.: Ergodicity of the $2$-D Navier-Stokes equation under random perturbations. Comm. Math. Phys. 172 (1995), no. 1, 119--141. MR1346374
  • Hairer, Martin and Mattingly, J.C.: Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing. Ann. of Math. (2) 164 (2006), no. 3, 993--1032. MR2259251
  • Hairer, Martin and Mattingly, J.C.: A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs. Electron. J. Probab. 16 (2011), no. 23, 658--738. MR2786645
  • Ichihara, Kanji and Kunita, Hiroshi.: A classification of the second order degenerate elliptic operators and its probabilistic characterization. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30 (1974), 235--254. MR0381007
  • Kliemann, Wolfgang.: Recurrence and invariant measures for degenerate diffusions. Ann. Probab. 15 (1987), no. 2, 690--707. MR0885138
  • Kusuoka, S. and Stroock, D.: Applications of the Malliavin calculus. III. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 2, 391--442. MR0914028
  • Rey-Bellet, Luc.: Ergodic properties of Markov processes. Open quantum systems. II, 1--39, Lecture Notes in Math., 1881, Springer, Berlin, 2006. MR2248986
  • Mattingly, J.C., Stuart, A.M. and Higham, D.J.: Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Stochastic Process. Appl. 101 (2002), no. 2, 185--232. MR1931266
  • Nualart, David.: The Malliavin calculus and related topics. Second edition. Probability and its Applications (New York). Springer-Verlag, Berlin, 2006. xiv+382 pp. ISBN: 978-3-540-28328-7; 3-540-28328-5 MR2200233
  • Protter, P.E.: Stochastic integration and differential equations. Second edition. Version 2.1. Corrected third printing. Stochastic Modelling and Applied Probability, 21. Springer-Verlag, Berlin, 2005. xiv+419 pp. ISBN: 3-540-00313-4 MR2273672
  • Revuz, D. and Yor, M.: Continuous Martingales and Brownian Motion, 3nd ed. Springer, (2005).
  • Shigekawa, Ichiro.: Stochastic analysis. Translated from the 1998 Japanese original by the author. Translations of Mathematical Monographs, 224. Iwanami Series in Modern Mathematics. American Mathematical Society, Providence, RI, 2004. xii+182 pp. ISBN: 0-8218-2626-3 MR2060917
  • Sheu, S.J.: Some estimates of the transition density of a nondegenerate diffusion Markov process. Ann. Probab. 19 (1991), no. 2, 538--561. MR1106275
  • Stettner, Łukasz.: Remarks on ergodic conditions for Markov processes on Polish spaces. Bull. Polish Acad. Sci. Math. 42 (1994), no. 2, 103--114. MR1810695
  • Talay, D.: Stochastic Hamiltonian systems: exponential convergence to the invariant measure, and discretization by the implicit Euler scheme. Inhomogeneous random systems (Cergy-Pontoise, 2001). Markov Process. Related Fields 8 (2002), no. 2, 163--198. MR1924934


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