Anticipated Generalized Backward Doubly Stochastic Differential Equations
Keyword(s):
In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two symmetric integrals related to two independent Brownian motions and an integral driven by a continuous increasing process but also include generators depending on the anticipated terms of the solution (Y, Z). Firstly, we prove the existence and uniqueness theorem for AGBDSDEs. Further, two comparison theorems are obtained after finding a new comparison theorem for GBDSDEs.
2011 ◽
Vol 27
(2)
◽
pp. 223-232
◽
2012 ◽
Vol 166-169
◽
pp. 3210-3213
◽
2012 ◽
Vol 67
(12)
◽
pp. 699-704
◽
2012 ◽
Vol 48
(4)
◽
pp. 899-917
◽