Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 2, p. 395-424

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.

Dans cet article, nous explicitons la dérivée du flot d'un processus de diffusion réfléchi. Nous obtenons des représentations stochastiques des dérivées des solutions de viscosité d'équations aux dérivées partielles paraboliques semi-linéaires. Nous en déduisons des représentations stochastiques des dérivées des solutions de viscosité d'inégalités variationnelles paraboliques avec conditions au bord de Neumann.

DOI : https://doi.org/10.1214/10-AIHP357
Classification:  60H10,  60H30,  35K55
Keywords: forward backward SDEs with refections, Feynman-Kac formulae, derivatives of the flows of reflected SDEs and BSDEs
@article{AIHPB_2011__47_2_395_0,
     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 = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {2},
     year = {2011},
     pages = {395-424},
     doi = {10.1214/10-AIHP357},
     zbl = {1236.60051},
     mrnumber = {2814416},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_2_395_0}
}
Bossy, Mireille; Cissé, Mamadou; Talay, Denis. Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 2, pp. 395-424. doi : 10.1214/10-AIHP357. http://www.numdam.org/item/AIHPB_2011__47_2_395_0/

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