Dirichlet prior for cascade SDE with Markov regime-switching

A Stochastic Differential Equation appearing in the statistical theory of turbulence is extended in random environment by assuming that its two parameters are switched by an unobserved continuoustime Markov chain whose states represent the states of the environment. A Dirichlet process is placed as a prior on the space of the sample paths of this chain, leading to a hierarchical Dirichlet model whose estimation is done both on simulated data and on real data of wind speed measured at the entrance of a mangrove ecosystem.