Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions

Mireille Bossy; Mamadou Cissé; Denis Talay

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

  • Volume: 47, Issue: 2, page 395-424
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Bossy, Mireille, Cissé, Mamadou, and 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 47.2 (2011): 395-424. <http://eudml.org/doc/240022>.

@article{Bossy2011,
abstract = {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.},
author = {Bossy, Mireille, Cissé, Mamadou, Talay, Denis},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {forward backward SDEs with refections; Feynman–Kac formulae; derivatives of the flows of reflected SDEs and BSDEs; stochastic differential equations with refection; reflected backward stochastic differential equations; Feynman-Kac formula; derivatives of flows of reflected SDEs and BSDEs},
language = {eng},
number = {2},
pages = {395-424},
publisher = {Gauthier-Villars},
title = {Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions},
url = {http://eudml.org/doc/240022},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Bossy, Mireille
AU - Cissé, Mamadou
AU - Talay, Denis
TI - Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 2
SP - 395
EP - 424
AB - 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.
LA - eng
KW - forward backward SDEs with refections; Feynman–Kac formulae; derivatives of the flows of reflected SDEs and BSDEs; stochastic differential equations with refection; reflected backward stochastic differential equations; Feynman-Kac formula; derivatives of flows of reflected SDEs and BSDEs
UR - http://eudml.org/doc/240022
ER -

References

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