Émery's inequality
functional Lipschitz coefficient
linear drift
localization
semimartingale
stochastic delay differential equation
variation-of-constants formula
On Émery's inequality and a variation-of-constants formula
Markus Riedle
Riedle
Markus
Markus Reiß
Reiß
Markus
Onno van Gaans
van Gaans
Onno
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 05-1
Markus Riedle
,
Markus Reiß,
Onno van Gaans
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 05-1
MSC 2000
- 60H20 Stochastic integral equations
-
60G48 Generalizations of martingales
-
34K50 Stochastic delay equations
Abstract
A generalization of Émery's inequality for stochastic integrals is shown for convolution integrals with respect to
an arbitrary semimartingale.
The inequality is used to
prove existence and uniqueness of solutions of equations of variation-of-constants type.
As a consequence, it is shown that the solution of a typical semilinear delay differential equation driven by a general semimartingale satisfies a variation-of-constants formula.
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