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Delay differential equations driven by Levy processes
 

Summary: Delay differential equations
driven by Levy processes
( joint work with M. Rei, O. van Gaans)
Markus Riedle
Humboldt University of Berlin
http://www.mathematik.hu-berlin.de/~riedle
Vilnius, 26 June 2006
Ornstein-Uhlenbeck process
dX(t) = aX(t) dt + dW(t), t 0,
X(0) = x
a R;
x R;
(W(t) : t 0) Wiener process. |u|>1
log |u| (du) < .
Theorem: The following are equivalent:
(1) there exists a unique stationary solution;
(2) the zero solution of
x(t) = ax(t) for t 0
is asymptotically stable.
1

  

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

 

Collections: Mathematics