Linear diffusion with stationary switching regime
Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2010)
ESAIM: Probability and Statistics
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Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other...