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An integral inequality for the invariant measure of some finite dimensional stochastic differential equation
1. | Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
References:
[1] |
V. I. Bogachev, N. V. Krylov and M. Röckner, On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions, Comm. Partial Differential Equations, 26 (2001), 2037-2080.
doi: 10.1081/PDE-100107815. |
[2] |
V. I. Bogachev, N. V. Krylov and M. Röckner, Regularity and global bounds for the densities of invariant measures of diffusion processes, (Russian) Dokl. Akad. Nauk, 405 (2005), 583-587. |
[3] |
G. Da Prato and A. Debussche, Ergodicity for the $3D$ stochastic Navier-Stokes equations, J. Math. Pures Appl., 82 (2003), 877-947.
doi: 10.1016/S0021-7824(03)00025-4. |
[4] |
G. Da Prato and A. Debussche, $m$-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise, Potential Anal, 26 (2007), 31-55.
doi: 10.1007/s11118-006-9021-5. |
[5] |
G. Da Prato and A. Debussche, Estimate for $P_tD$ for the stochastic Burgers equation, Ann. Inst. Henri Poincaré Probab. Stat., 52 (2016), 1248-1258.
doi: 10.1214/15-AIHP685. |
[6] |
G. Da Prato and J. Zabczyk, Ergodicity for Infinite-Dimensional Systems, London Mathematical Society Lecture Note Series, 229. Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511662829. |
[7] |
G. Da Prato and J. Zabczyk, Differentiability of the Feynman-Kac semigroup and a control application, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 8 (1997), 183-188. |
[8] |
K. D. Elworthy, Stochastic flows on Riemannian manifolds, in Diffusion processes and related problems in analysis, Vol. II, M. A. Pinsky and V. Wihstutz (eds.), Birkhäuser, 33-72, 1992. MR1187985 Reviewed Elworthy, K. D. Stochastic flows on Riemannian manifolds. Diffusion processes and related problems in analysis, Vol. II (Charlotte, NC, 1990), 37-72, Progr. Probab., 27, Birkhäuser Boston, Boston, MA, 1992. 58G32 (60H10). |
[9] |
N. V. Krylov, Introduction to the Theory of Diffusion Processes, Translations of Mathematical Monographs, 142, 1995. |
[10] |
P. Malliavin, Stochastic Analysis, Springer-Verlag, 1997.
doi: 10.1007/978-3-642-15074-6. |
[11] |
G. Metafune, D. Pallara and A. Rhandi, Global properties of invariant measures, J. Funct. Analysis, 223 (2005), 396-424.
doi: 10.1016/j.jfa.2005.02.001. |
[12] |
D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, 1995.
doi: 10.1007/978-1-4757-2437-0. |
show all references
References:
[1] |
V. I. Bogachev, N. V. Krylov and M. Röckner, On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions, Comm. Partial Differential Equations, 26 (2001), 2037-2080.
doi: 10.1081/PDE-100107815. |
[2] |
V. I. Bogachev, N. V. Krylov and M. Röckner, Regularity and global bounds for the densities of invariant measures of diffusion processes, (Russian) Dokl. Akad. Nauk, 405 (2005), 583-587. |
[3] |
G. Da Prato and A. Debussche, Ergodicity for the $3D$ stochastic Navier-Stokes equations, J. Math. Pures Appl., 82 (2003), 877-947.
doi: 10.1016/S0021-7824(03)00025-4. |
[4] |
G. Da Prato and A. Debussche, $m$-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise, Potential Anal, 26 (2007), 31-55.
doi: 10.1007/s11118-006-9021-5. |
[5] |
G. Da Prato and A. Debussche, Estimate for $P_tD$ for the stochastic Burgers equation, Ann. Inst. Henri Poincaré Probab. Stat., 52 (2016), 1248-1258.
doi: 10.1214/15-AIHP685. |
[6] |
G. Da Prato and J. Zabczyk, Ergodicity for Infinite-Dimensional Systems, London Mathematical Society Lecture Note Series, 229. Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511662829. |
[7] |
G. Da Prato and J. Zabczyk, Differentiability of the Feynman-Kac semigroup and a control application, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 8 (1997), 183-188. |
[8] |
K. D. Elworthy, Stochastic flows on Riemannian manifolds, in Diffusion processes and related problems in analysis, Vol. II, M. A. Pinsky and V. Wihstutz (eds.), Birkhäuser, 33-72, 1992. MR1187985 Reviewed Elworthy, K. D. Stochastic flows on Riemannian manifolds. Diffusion processes and related problems in analysis, Vol. II (Charlotte, NC, 1990), 37-72, Progr. Probab., 27, Birkhäuser Boston, Boston, MA, 1992. 58G32 (60H10). |
[9] |
N. V. Krylov, Introduction to the Theory of Diffusion Processes, Translations of Mathematical Monographs, 142, 1995. |
[10] |
P. Malliavin, Stochastic Analysis, Springer-Verlag, 1997.
doi: 10.1007/978-3-642-15074-6. |
[11] |
G. Metafune, D. Pallara and A. Rhandi, Global properties of invariant measures, J. Funct. Analysis, 223 (2005), 396-424.
doi: 10.1016/j.jfa.2005.02.001. |
[12] |
D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, 1995.
doi: 10.1007/978-1-4757-2437-0. |
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