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

DOI10.1214/10-AIHP357zbMath1236.60051MaRDI QIDQ537129

Mireille Bossy, Mamadou Cissé, Denis Talay

Publication date: 19 May 2011

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/240022

zbMATH Keywords

Feynman-Kac formulareflected backward stochastic differential equationsderivatives of flows of reflected SDEs and BSDEsstochastic differential equations with refection

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear parabolic equations (35K55) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items

Maximum principle for stochastic control of SDEs with measurable drifts ⋮ Multivalued monotone stochastic differential equations with jumps ⋮ Pathwise differentiability of reflected diffusions in convex polyhedral domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• Dérivation stochastique de diffusions réfléchies. (Stochastic derivatives of diffusions with reflections)
• Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• Generalized BSDEs and nonlinear Neumann boundary value problems
• Representation theorems for backward stochastic differential equations
• Euler's approximations of solutions of SDEs with reflecting boundary.
• An explicit formula for the Skorokhod map on \([0,a\)]
• Representations and regularities for solutions to BSDEs with reflections
• Regularity and representation of viscosity solutions of partial differential equations via backward stochastic differential equations
• The Malliavin Calculus and Related Topics
• Reflected forward-backward SDEs and obstacle problems with boundary conditions