Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients
Romain Abraham; Olivier Riviere
ESAIM: Probability and Statistics (2006)
- Volume: 10, page 184-205
- ISSN: 1292-8100
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topAbraham, Romain, and Riviere, Olivier. "Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients." ESAIM: Probability and Statistics 10 (2006): 184-205. <http://eudml.org/doc/249748>.
@article{Abraham2006,
abstract = {
We consider a system of fully coupled forward-backward stochastic
differential equations. First we generalize the results of
Pardoux-Tang [7] concerning the regularity of the solutions with
respect to initial conditions. Then, we prove that in some particular
cases this system leads to a
probabilistic representation of solutions of a second-order PDE whose
second order coefficients depend on the gradient of the solution. We
then give some examples in dimension 1 and dimension 2 for which the
assumptions are easy to check.
},
author = {Abraham, Romain, Riviere, Olivier},
journal = {ESAIM: Probability and Statistics},
keywords = {Forward-backward stochastic differential equations; partial differential equations.; forward-backward stochastic differential equations; partial differential equations},
language = {eng},
month = {3},
pages = {184-205},
publisher = {EDP Sciences},
title = {Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients},
url = {http://eudml.org/doc/249748},
volume = {10},
year = {2006},
}
TY - JOUR
AU - Abraham, Romain
AU - Riviere, Olivier
TI - Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients
JO - ESAIM: Probability and Statistics
DA - 2006/3//
PB - EDP Sciences
VL - 10
SP - 184
EP - 205
AB -
We consider a system of fully coupled forward-backward stochastic
differential equations. First we generalize the results of
Pardoux-Tang [7] concerning the regularity of the solutions with
respect to initial conditions. Then, we prove that in some particular
cases this system leads to a
probabilistic representation of solutions of a second-order PDE whose
second order coefficients depend on the gradient of the solution. We
then give some examples in dimension 1 and dimension 2 for which the
assumptions are easy to check.
LA - eng
KW - Forward-backward stochastic differential equations; partial differential equations.; forward-backward stochastic differential equations; partial differential equations
UR - http://eudml.org/doc/249748
ER -
References
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- E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic pdes. Probab. Th. Rel. Fields114 (1999) 123–150.
- P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell.12 (1990) 629–639.
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