2004
DOI: 10.1007/s00028-003-0078-y
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A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions

Abstract: 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 0,Here A is the generator of a C 0 −semigroup on a separable real Banach space E and {W (t)} t 0 is an E-valued Brownian motion.

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Cited by 10 publications
(7 citation statements)
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“…In order to treat transition semigroups on C b (E), several approaches have been proposed in the literature. We mention the theory of weakly continuous semigroups of Cerrai [6], the theory of bi-continuous semigroups of Kühnemund [18], see also [9,19] for applications in the context of transition semigroups, and the theory of π-semigroups by Priola [25]. It should be noted that in these approaches additional assumptions, in particular continuity and equicontinuity assumptions, are made which ensure that a Riemann integral can be used to compute the Laplace transform.…”
Section: Introductionmentioning
confidence: 99%
“…In order to treat transition semigroups on C b (E), several approaches have been proposed in the literature. We mention the theory of weakly continuous semigroups of Cerrai [6], the theory of bi-continuous semigroups of Kühnemund [18], see also [9,19] for applications in the context of transition semigroups, and the theory of π-semigroups by Priola [25]. It should be noted that in these approaches additional assumptions, in particular continuity and equicontinuity assumptions, are made which ensure that a Riemann integral can be used to compute the Laplace transform.…”
Section: Introductionmentioning
confidence: 99%
“…In comparison to other constructions of semigroups on weighted function spaces using locally convex topologies and the concept of bicontinuous semigroups (cf. [36] and the references therein), we emphasize that our spaces are (separable) Banach spaces so, as spaces with one single norm, are easier to handle.…”
mentioning
confidence: 99%
“…This semigroup is extensively studied by many authors, we refer to Da Prato [3][4][5], Da Prato and Zabczyk [6][7][8], Goldys and Kocan [12], Kühnemund and van Neerven [16], Lunardi [18], Metafune et al [19], Priola [20], Rhandi [22], van Neerven [23] and van Neerven and Zabczyk [24]. The proposition below will be useful in the following and can be found, e.g., in Cerrai [2].…”
Section: The Ornstein-uhlenbeck Semigroupmentioning
confidence: 95%