A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE
Lejay, Antoine
HAL, inria-00001228 / Harvested from HAL
Text on HAL
We extend some results on time-homogeneous processes generated by divergence form operators to time-inhomogeneous ones. These results concern the decomposition of such processes as Dirichlet process, with an explicit expression for the term of zero-quadratic variation. Moreover, we extend some results on the Itô formula and BSDEs related to weak solutions of PDEs, and we study the case of quasi-linear PDEs. Finally, our results are used to prove the existence of weak solutions to forward–backward stochastic differential equations.
Publié le : 2004-07-05
Classification:  Quasi-linear PDE,  Divergence form-operator,  Forward–backward stochastic differential equation,  Time reversal of a diffusion,  Dirichlet process,  AMS: 60H10; (35J60; 35R60; 60J60),  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{inria-00001228,
     author = {Lejay, Antoine},
     title = {A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00001228}
}

Lejay, Antoine. A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/inria-00001228/