252 research outputs found
The obstacle problem for quasilinear stochastic PDE's
We prove an existence and uniqueness result for the obstacle problem of
quasilinear parabolic stochastic PDEs. The method is based on the probabilistic
interpretation of the solution by using the backward doubly stochastic
differential equation.Comment: Published in at http://dx.doi.org/10.1214/09-AOP507 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Numerical Computation for Backward Doubly SDEs with random terminal time
In this article, we are interested in solving numerically backward doubly
stochastic differential equations (BDSDEs) with random terminal time tau. The
main motivations are giving a probabilistic representation of the Sobolev's
solution of Dirichlet problem for semilinear SPDEs and providing the numerical
scheme for such SPDEs. Thus, we study the strong approximation of this class of
BDSDEs when tau is the first exit time of a forward SDE from a cylindrical
domain. Euler schemes and bounds for the discrete-time approximation error are
provided.Comment: 38, Monte Carlo Methods and Applications (MCMA) 201
Stochastic partial differential equations with singular terminal condition
In this paper, we first prove existence and uniqueness of the solution of a
backward doubly stochastic differential equation (BDSDE) and of the related
stochastic partial differential equation (SPDE) under monotonicity assumption
on the generator. Then we study the case where the terminal data is singular,
in the sense that it can be equal to + on a set of positive measure. In
this setting we show that there exists a minimal solution, both for the BDSDE
and for the SPDE. Note that solution of the SPDE means weak solution in the
Sobolev sense
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