The transport equation and zero quadratic variation processes

Jorge Clarke de La Cerda (1, 2) , Christian Olivera (3) , Ciprian Tudor (2)

1 Departamento de Matematica [Valparaiso]
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]

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.

Mots clés: method of characteristics; Malliavin calculus; fractional Brownian motion; Hermite process; zero quadratic variation process; existence of density; stochastic calculus via regulararization; Transport equation

Domaines: Probabilités [math.PR]

Jorge Clarke de La Cerda, Christian Olivera, Ciprian Tudor. The transport equation and zero quadratic variation processes. Discrete and Continuous Dynamical Systems - Series B, 2016, ⟨10.3934/xx.xx.xx.xx⟩. ⟨hal-01690248⟩