Abstract
We present a semigroup approach to stochastic delay equations of the form
in the space of continuous functions C[-h,0]. We represent the solution as a C[-h,0]-valued process arising from a stochastic weak*-integral in the bidual C[-h,0]** and show how this process can be interpreted as a mild solution of an associated stochastic abstract Cauchy problem. We obtain a necessary and sufficient condition guaranteeing the existence of an invariant measure.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Neerven, J., Riedle, M. A Semigroup Approach to Stochastic Delay Equations in Spaces of Continuous Functions. Semigroup Forum 74, 227–239 (2007). https://doi.org/10.1007/s00233-005-0649-7
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DOI: https://doi.org/10.1007/s00233-005-0649-7