Abstract
We prove a Lie-Trotter product formula for the Ornstein--Uhlenbeck semigroup associated with the stochastic linear Cauchy problem \( dX(t) = AX(t)\,dt + dW(t), t \leq 0,\\ X(0) = x_0. \) Here A is the generator of a C 0-semigroup on a separable real Banach space E and \( \{W(t)\}_{t\leq 0} \) is an E-valued Brownian motion.
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