## 2007.166: On Émery's Inequality and a Variation-of-Constants Formula

2007.166:
Markus Reiß, Markus Riedle and Onno van Gaans
(2007)
*On Émery's Inequality and a Variation-of-Constants Formula.*
Stochastic Analysis and Applications, 25 (2).
pp. 353-379.
ISSN 1532-9356

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DOI: 10.1080/07362990601139586

## Abstract

A generalization of Émery's inequality for stochastic integrals is shown for convolution integrals of the form $\left( \int_0^t g(t-s) Y(s-) dZ(s)\right)_{t \geq 0}$, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. An even more general inequality for processes with two parameters is proved. 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 semilinear delay differential equation with functional Lipschitz diffusion coefficient and driven by a general semimartingale satisfies a variation-of-constants formula.

Item Type: | Article |
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Uncontrolled Keywords: | Émery's inequality; Functional Lipschitz coefficient; Linear drift; Semimartingale; Stochastic delay differential equation; Variation-of-constants formula |

Subjects: | MSC 2000 > 34 Ordinary differential equations MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2007.166 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 19 November 2007 |

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