# First Order Linear Marcus SPDEs

## TL;DR

This paper solves a Levy-driven linear stochastic first-order PDE using stochastic characteristics, providing a solution form similar to deterministic PDEs and Brownian-driven SPDEs, advancing understanding of Levy noise in stochastic transport equations.

## Contribution

It introduces a method to solve Levy-driven linear stochastic PDEs in Marcus form, extending classical solutions to include Levy noise.

## Key findings

- Solution expressed via stochastic characteristics
- Equivalent form to deterministic PDE solutions
- Applicable to Levy-driven stochastic transport equations

## 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).