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 |
|---|---|
| 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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