Differentiability of transition semigroup of generalized Ornstein-Uhlenbeck process: a probabilistic approach
Ben Goldys and Szymon Peszat
Abstract
Let , be the
transition semigroup on the space of bounded
measurable functions on a Banach space , of the Markov
family defined by the linear equation with additive noise We give a simple probabilistic proof of the fact that
null-controlla\-bility of the corresponding deterministic system
implies that for any ,
is infinitely many times Fréchet differentiable and that
where
is the symmetric n-fold Itô
integral of the controls .
Keywords:
Gradient estimates, Ornstein–Uhlenbeck processes, strong Feller property, hypoelliptic diffusions, noise on boundary.
AMS Subject Classification:
Primary 60H10; secondary 60H15 60H17, 35B30, 35G15.