Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformly gamma-radonifying families of operators and and the stochastic
  Weiss conjecture   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.

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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an