BDSDEs with Markov Chains and applications in Markovian-Switching LQ problems for backward doubly stochastic system

In this paper, we introduce a new type of BDSDEs with Markov Chains. We also consider the backward doubly stochastic systems with Markovian-Switching described by the BDSDEs with Markov Chains and obtain the unique optimal control for the stochastic switching LQ problems.