DCDS-B
The transport equation and zero quadratic variation processes
Jorge Clarke Christian Olivera Ciprian Tudor
Discrete & Continuous Dynamical Systems - B 2016, 21(9): 2991-3002 doi: 10.3934/dcdsb.2016083
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.
keywords: Malliavin calculus method of characteristics stochastic calculus via regularization fractional Brownian motion existence of density. Hermite process Transport equation zero quadratic variation process

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