Stochastic integration in locally convex spaces
stochastic delay equations in spaces of continuous functions
invariant measures
Solutions of stochastic delay equations in spaces of continuous functions
Markus Riedle
Riedle
Markus
Jan M. A. M. vanNeerven
vanNeerven
Jan M. A. M.
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 18-2005, 11
Markus Riedle
,
Jan M. A. M. vanNeerven
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 18-2005, 11
MSC 2000
- 34K50 Stochastic delay equations
-
34F05 Equations and systems with randomness
-
47D06 One-parameter semigroups and linear evolution equations
-
60H05 Stochastic integrals
Abstract
We present a semigroup approach to stochastic delay equations
with linear drift and additive noise
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$\s$-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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