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A two-dimensinal Markov process $\{\theta_{t},S_{t}\}_{t=1}^{\infty}$ where $\theta_{t} \in \Theta$ and $S_{t} \in S$.$\Theta$ is a continuous state space and $S$ is a discrete state space. Suppose I know: $$P(\theta_{t+1}\in \Theta_{0} \subset \Theta, S_{t+1}=s \in S|(\theta_{t},S_{t}))$$

Can I use some tools similar with stationary distribution in one-dimensional Markov process to analyze this process? Can some guys propose some ideas or recommend references?

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