Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II

Viorel Barbu; Giuseppe Da Prato; Luciano Tubaro

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 699-724
  • ISSN: 0246-0203

Abstract

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This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.

How to cite

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Barbu, Viorel, Da Prato, Giuseppe, and Tubaro, Luciano. "Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 699-724. <http://eudml.org/doc/239225>.

@article{Barbu2011,
abstract = {This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.},
author = {Barbu, Viorel, Da Prato, Giuseppe, Tubaro, Luciano},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Neumann problem; Ornstein–Uhlenbeck operator; Kolmogorov operator; reflection problem; infinite-dimensional analysis; Ornstein-Uhlenbeck operator},
language = {eng},
number = {3},
pages = {699-724},
publisher = {Gauthier-Villars},
title = {Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II},
url = {http://eudml.org/doc/239225},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Barbu, Viorel
AU - Da Prato, Giuseppe
AU - Tubaro, Luciano
TI - Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 699
EP - 724
AB - This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.
LA - eng
KW - Neumann problem; Ornstein–Uhlenbeck operator; Kolmogorov operator; reflection problem; infinite-dimensional analysis; Ornstein-Uhlenbeck operator
UR - http://eudml.org/doc/239225
ER -

References

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  1. [1] L. Ambrosio, G. Savaré and L. Zambotti. Existence and stability for Fokker–Planck equations with log-concave reference measure. Probab. Theory Related Fields. 145 (2009) 517–564. Zbl1235.60105MR2529438
  2. [2] V. Barbu and G. Da Prato. The Neumann problem on unbounded domains of ℝd and stochastic variational inequalities. Comm. PDE 30 (2005) 1217–1248. Zbl1130.35137MR2180301
  3. [3] V. Barbu and G. Da Prato. The generator of the transition semigroup corresponding to a stochastic variational inequality. Comm. PDE 33 (2008) 1318–1338. Zbl1155.60034MR2450160
  4. [4] V. Barbu, G. Da Prato and L. Tubaro. Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. Ann. Probab. 37 (2009) 1427–1458. Zbl1205.60141MR2546750
  5. [5] V. I. Bogachev. Gaussian Measures. Mathematical Surveys and Monographs 62. Amer. Math. Soc., Providence, RI, 1998. Zbl0913.60035MR1642391
  6. [6] E. Cepà. Problème de Skorohod multivoque. Ann. Probab. 26 (1998) 500–532. Zbl0937.34046MR1626174
  7. [7] G. Da Prato. Kolmogorov Equations for Stochastic PDEs. Birkhäuser, Basel, 2004. Zbl1066.60061MR2111320
  8. [8] G. Da Prato and A. Lunardi. Elliptic operators with unbounded drift-coefficients and Neumann boundary condition. J. Differential Equations 198 (2004) 35–52. Zbl1046.35025MR2037749
  9. [9] G. Da Prato and J. Zabczyk. Ergodicity for Infinite Dimensional Systems. London Mathematical Society Lecture Notes 229. Cambridge Univ. Press, 1996. Zbl0849.60052MR1417491
  10. [10] G. Da Prato and J. Zabczyk. Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Notes 293. Cambridge Univ. Press, 2002. Zbl1012.35001MR1985790
  11. [11] A. Hertle. Gaussian surface measures and the Radon transform on separable Banach spaces. In Measure Theory, Oberwolfach 1979 (Proc. Conf., Oberwolfach, 1979) 513–531. Lecture Notes in Math. 794. Springer, Berlin, 1980. Zbl0431.28011MR577995
  12. [12] P. Malliavin. Stochastic Analysis. Springer, Berlin, 1997. Zbl0878.60001MR1450093
  13. [13] P. A. Meyer and W. A. Zheng. Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré 20 (1984) 353–372. Zbl0551.60046MR771895
  14. [14] D. Nualart and E. Pardoux. White noise driven by quasilinear SPDE’s with reflection. Probab. Theory Related Fields 93 (1992) 77–89. Zbl0767.60055MR1172940
  15. [15] A. V. Skorohod. Integration in Hilbert Space. Springer, New York, 1974. MR466482
  16. [16] L. Zambotti. Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection. Probab. Theory Related Fields 123 (2002) 579–600. Zbl1009.60047MR1921014

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