# L\'{e}vy driven CARMA generalized processes and stochastic partial differential equations

## TL;DR

This paper introduces a new framework for Lévy driven CARMA random fields via SPDEs, unifying existing definitions and extending classical CARMA processes to higher dimensions.

## Contribution

It provides a novel definition of Lévy driven CARMA random fields as solutions to SPDEs and establishes conditions for their existence, connecting various prior models.

## Key findings

- Unified framework for CARMA random fields and SPDEs
- Conditions for existence of mild solutions
- Extension of classical CARMA processes to higher dimensions

## Abstract

We give a new definition of a L\'{e}vy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of our SPDE. Our model finds a connection between all known definitions of CARMA random fields, and especially for dimension 1 we obtain the classical CARMA process.