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arXiv · 2303.00674

First Order Linear Marcus SPDEs

Lena-Susanne Hartmann·Ilya Pavlyukevich
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Abstract

In this paper we solve a L\'evy driven linear stochastic first order partial differential equation (transport equation) understood in the canonical (Marcus) form. The solution can be obtained with the help of the method of stochastic characteristics. It has the same form as a solution of a deterministic PDE or a solution of a stochastic PDE driven by a Brownian motion studied by Kunita (1984, 1997).

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Lena-Susanne Hartmann, Ilya Pavlyukevich. 2023-03-01. First Order Linear Marcus SPDEs. https://arxiv.org/abs/2303.00674

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