# Piecewise deterministic Markov processes driven by scalar conservation laws

## TL;DR

This paper studies PDMPs driven by scalar conservation laws, establishing existence and bounded variation of sample paths, and applies the framework to production and traffic models with data-driven flux variations.

## Contribution

It introduces a novel PDMP framework driven by scalar conservation laws and demonstrates its applicability to real-world production and traffic systems.

## Key findings

- Existence of PDMPs under certain conditions
- Bounded variation estimates for sample paths
- Effective modeling of flux scattering in data

## Abstract

We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which assumptions we can guarantee the existence of a PDMP and conclude bounded variation estimates for sample paths. Finally, we apply this dynamics to a production and traffic model and use this framework to incorporate the well-known scattering of flux functions observed in data sets.