Pathwise differentiability for SDEs in a convex polyhedron with oblique reflection
Annales de l'I.H.P. Probabilités et statistiques (2009)
- Volume: 45, Issue: 1, page 104-116
- ISSN: 0246-0203
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] H. Airault. Perturbations singulières et solutions stochastiques de problèmes de D. Neumann–Spencer. J. Math. pures et appl. 55 (1976) 233–268. Zbl0349.60062MR501184
- [2] K. Burdzy and Z.-Q. Chen. Coalescence of synchronous couplings. Probab. Theory Related Fields 123 (2002) 553–578. Zbl1004.60080MR1921013
- [3] K. L. Chung and R. J. Williams. Introduction to Stochastic Integration, 2nd edition. Birkhäuser, Boston, 1990. Zbl0725.60050MR1102676
- [4] J.-D. Deuschel and L. Zambotti. Bismut–Elworthy formula and random walk representation for SDEs with reflection. Stochastic Process. Appl. 115 (2005) 907–925. Zbl1071.60044MR2134484
- [5] P. Dupuis and H. Ishii. On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics 35 (1991) 31–62. Zbl0721.60062MR1110990
- [6] P. Dupuis and H. Ishii. SDEs with oblique reflection on nonsmooth domains. Ann. Probab. 21 (1993) 554–580. Zbl0787.60099MR1207237
- [7] P. L. Lions and A. S. Sznitman. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984) 511–537. Zbl0598.60060MR745330
- [8] A. Mandelbaum and K. Ramanan. Directional derivatives of oblique reflection maps. Preprint, 2005.
- [9] D. Revuz and M. Yor. Continuous Martingales and Brownian Motion, 3rd edition. Springer, Heidelberg, 2005. Zbl1087.60040
- [10] L. C. G. Rogers and D. Williams. Diffusions, Markov Processes and Martingales, Vol. 2. Cambridge Univ. Press, 2000. Zbl0977.60005MR1780932
- [11] H. Tanaka. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J. 9 (1979) 163–177. Zbl0423.60055MR529332
- [12] S. R. S. Varadhan and R. J. Williams. Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. 38 (1984) 405–443. Zbl0579.60082MR792398