A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions
The authors prove a Lie-Trotter product formula for the Orenstein-Uhlenbeck semigroup associated with the stochastic linear Cauchy problem \[ \begin{aligned} dX(t) &= AX(t)\,dt+ dW(t),\quad t\geq 0,\\ X(0) &= x_0,\end{aligned} \] where \(A\) is the generator of a \(C_0\)-semigroup on a separable real Banach space \(E\) and \(\{W(t)\}_{t\geq 0}\) is an \(E\)-valued Brownian motion.
scientific article; zbMATH DE number 2111542