On Regularity Property of Retarded Ornstein–Uhlenbeck Processes in Hilbert Spaces

Kai Liu ()
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Kai Liu: The University of Liverpool

Journal of Theoretical Probability, 2012, vol. 25, issue 2, 565-593

Abstract: Abstract In this work, some regularity properties of mild solutions for a class of stochastic linear functional differential equations driven by infinite-dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a class of stochastic convolutions which naturally arise in the solutions and investigate their Yosida approximants. By means of the retarded fundamental solutions, we find conditions under which each mild solution permits a continuous modification. With the aid of Yosida approximation, we study two kinds of regularity properties, temporal and spatial ones, for the retarded solution processes. By employing a factorization method, we establish a retarded version of the Burkholder–Davis–Gundy inequality for stochastic convolutions.

Keywords: Fundamental solution; Yosida approximation; Burkholder–Davis–Gundy inequality; 60H15; 60G15; 60H05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0374-3

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