In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.
Publié le : 2011-05-15
Classification:
Forward backward SDEs with refections,
Feynman–Kac formulae,
Derivatives of the flows of reflected SDEs and BSDEs,
60H10,
60H30,
35K55
@article{1300887275,
author = {Bossy, Mireille and Ciss\'e, Mamadou and Talay, Denis},
title = {Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 395-424},
language = {en},
url = {http://dml.mathdoc.fr/item/1300887275}
}
Bossy, Mireille; Cissé, Mamadou; Talay, Denis. Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 395-424. http://gdmltest.u-ga.fr/item/1300887275/