Backward doubly stochastic differential equations with jumps and stochastic partial differential-integral equations

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 jum...

On Solving Backward Doubly Stochastic Differential Equations

Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations...

Stochastic Differential Equations with Jumps

Gradient estimates and a Harnack inequality are established for the semigroup associated to stochastic differential equations driven by Poisson processes. As applications, estimates of the transition probability density, the compactness and ultraboundedness of the semigroup are studied in terms of the corresponding invariant measure.

Stochastic differential equations with jumps,

This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions. Subject classifications: Primary 60H10; Secondary 60H30, 60J75