ORNSTEIN-UHLENBECK TYPE OPERATORS INDUCED BY SOME GEOMETRIC STRUCTURES ON COMPLEX DOMAINS

Using geometric structures’s models, we present the AiraultJendoubi-Ouerdiane approach for constructing Ornstein-Uhlenbeck type operator induced by geometric structures on complex domains. From a probabilistic point of view, this operator appeared in the Langevin equation as the generator of the Euclidean Ornstein-Uhlenbeck process which described a perturbation of a Brownian motion (the heat semigroup). We explain this method via the Berezin-Bergman-Poincar´e model.