The transport equation and zero quadratic variation processes

Jorge  Clarke; Christian  Olivera; Ciprian  Tudor

doi:10.3934/dcdsb.2016083

Article Contents

2016, Volume 21, Issue 9: 2991-3002. Doi: 10.3934/dcdsb.2016083

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The transport equation and zero quadratic variation processes

1.
Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España 1680, Valparaíso
2.
Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970-Campinas-SP
3.
Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d'Ascq

Received: September 30, 2015

Revised: December 31, 2015

Published: October 2016

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Abstract

We analyze the transport equation driven by a zero quadratic variation process. Using the stochastic calculus via regularization and the Malliavin calculus techniques, we prove the existence, uniqueness and absolute continuity of the law of the solution. As an example, we discuss the case when the noise is a Hermite process.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 60H05, 60H07.

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