Multi-Dimensional Reflected Backward Stochastic Differential Equations And The Comparison Theorem As Well As Continuous Coefficient: An Existence Result

In this paper,we generalize the result of multi-dimensional RBSDE with one barrier to the case of two reflecting barriers.The existence and uniqueness result of the solution was firstly proved by the fixed point argument where the every element of the solution is forced to stay between the respective given stochastic processes,ie.multi-dimensional obstacles. We also give one kind of multi-dimensional comparison theorem of Y.In the last two parts of the paper,we focused on K,the process to pull the solution above (or between)the obstacle(two obstacles).We first use the method similar with that in EL.karoui[1] to get the comparison theorem of K in the case of one reflecting barrier,At last,we use the idea of penalization to prove one existence result of the solution for the multi-dimensional RBSDE where the coefficient is continuous and has the linear growth,this also help us to give the comparison theorem of K~+ and K~- in the case of two reflecting barriers.