233 research outputs found
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
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
A Class of Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients
In this work the existence of solutions of one-dimensional backward dou- bly
stochastic differential equations (BDSDEs in short) where the coefficient is
left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also,
the associated comparison theorem is obtained.Comment: 15 page
On Backward Doubly Stochastic Differential Evolutionary System
In this paper, we are concerned with backward doubly stochastic differential
evolutionary systems (BDSDESs for short). By using a variational approach based
on the monotone operator theory, we prove the existence and uniqueness of the
solutions for BDSDESs. We also establish an It\^o formula for the Banach
space-valued BDSDESs.Comment: 33 page
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