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• W1620184481 abstract "We introduce the notion of uniform gamma-radonification of a family of operators, which unifies the notions of R-boundedness of a family of operators and gamma-radonification of an individual operator. We study the the properties of uniformly gamma-radonifying families of operators in detail and apply our results to the stochastic abstract Cauchy problem $dU(t) = AU(t) dt + B dW(t); U(0) = 0$ Here, $A$ is the generator of a strongly continuous semigroup of operators on a Banach space $E$, $B$ is a bounded linear operator from a separable Hilbert space $H$ into $E$, and $W$ is an $H$-cylindrical Brownian motion. When $A$ and $B$ are simultaneously diagonalisable, we prove that an invariant measure exists if and only if the family $ {sqrt{lambda} R(lambda, A)B : lambda > 0} $ is uniformly gamma-radonifying. This result can be viewed as a partial solution of a stochastic version of the Weiss conjecture in linear systems theory." @default.
• W1620184481 created "2016-06-24" @default.
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• W1620184481 date "2006-11-23" @default.
• W1620184481 modified "2023-09-27" @default.
• W1620184481 title "Uniformly gamma-radonifying families of operators and and the stochastic Weiss conjecture" @default.
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