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Ornstein-Uhlenbeck semigroups on Banach spaces generated by
 

Summary: Ornstein-Uhlenbeck semigroups on Banach spaces
generated by
stochastic differential equations with delay
Markus Riedle
Humboldt-University of Berlin
Leiden, 22 June 2004
Overview
1) Example
2) General formulation of the problem
3) Results
1
Example (1)
X(t, )= X(0, ) +
t
0 [-r,0]
X(s + u, ) (du) ds + W(t, ), t 0,
X(u, )= (u), u [-r, 0], for all
where W is a real-valued Wiener process on (, A, P),
is a finite signed measure,
C([-r, 0]) := { : [-r, 0] R continuous}

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics