Abstract
By replacing the final condition for backward stochastic differential equations (in short: BSDEs) by a stationarity condition on the solution process we introduce a new class of BSDEs. In a natural manner we associate to such BSDEs the solution of ergodic second order partial differential equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Barles, R. Buckdahn and E. Pardoux, BSDE’s and integral-partial differential equations, preprint.
A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978.
J. M. Bismut, An introductory approach to duality in optimal stochastic control, SIAM Rev., 20 (1) (1978), 62–78.
M. G. Crandall, H. Ishii and P. L. Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Soc, 27 (1992), 1–67.
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Berlin New York Heidelberg: Springer, 1977.
J. Ishii and S. Koike, Viscosity solutions for monotone systems of second order elliptic PDE’s, Commun, in Partial Diff. Equ., 16 (6–7) (1991), 1095–1128.
E. Pardoux and S. Peng, Adapted solutions of backward stochastic differential equations, Systems and Control Letters, 14 (1990).
E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, in: B. L. Rozovskii and R. B. Sowers, Eds., Stochastic Partial Differential Equations and their Applications, Lect. Notes Control Inf. Sci. 176, Springer, Berlin Heidelberg New York, (1992), 200–217.
S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastics Reports, 37 (1991), 61–74.
S. Peng, A generalized programming principle and Hamilton-Jacobi-Bellman equation, Stochastics and Stochastics Reports, 38 (1992), 119–134.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Basel AG
About this paper
Cite this paper
Buckdahn, R., Peng, S. (1999). Ergodic Backward SDE and Associated PDE. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8681-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8681-9_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9727-3
Online ISBN: 978-3-0348-8681-9
eBook Packages: Springer Book Archive