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

On Émery's inequality and a variation-of-constants formula

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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