2,652 research outputs found
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
On the discretization of backward doubly stochastic differential equations
In this paper, we are dealing with the approximation of the process (Y,Z)
solution to the backward doubly stochastic differential equation with the
forward process X . After proving the L2-regularity of Z, we use the Euler
scheme to discretize X and the Zhang approach in order to give a discretization
scheme of the process (Y,Z)
Forward-Backward Doubly Stochastic Differential Equations with Random Jumps and Stochastic Partial Differential-Integral Equations
In this paper, we study forward-backward doubly stochastic differential
equations driven by Brownian motions and Poisson process (FBDSDEP in short).
Both the probabilistic interpretation for the solutions to a class of
quasilinear stochastic partial differential-integral equations (SPDIEs in
short) and stochastic Hamiltonian systems arising in stochastic optimal control
problems with random jumps are treated with FBDSDEP. Under some monotonicity
assumptions, the existence and uniqueness results for measurable solutions of
FBDSDEP are established via a method of continuation. Furthermore, the
continuity and differentiability of the solutions of FBDSDEP depending on
parameters is discussed. Finally, the probabilistic interpretation for the
solutions to a class of quasilinear SPDIEs is given
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
Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles
We introduce a discrete time reflected scheme to solve doubly reflected
Backward Stochastic Differential Equations with jumps (in short DRBSDEs),
driven by a Brownian motion and an independent compensated Poisson process. As
in Dumitrescu-Labart (2014), we approximate the Brownian motion and the Poisson
process by two random walks, but contrary to this paper, we discretize directly
the DRBSDE, without using a penalization step. This gives us a fully
implementable scheme, which only depends on one parameter of approximation: the
number of time steps (contrary to the scheme proposed in Dumitrescu-Labart
(2014), which also depends on the penalization parameter). We prove the
convergence of the scheme, and give some numerical examples.Comment: arXiv admin note: text overlap with arXiv:1406.361
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