# Cylindrical Martingale Problems Associated with L\'evy Generators

## TL;DR

This paper explores cylindrical martingale problems linked to Lévy generators in Banach spaces, establishing their relation to SPDE solutions and providing existence and uniqueness results.

## Contribution

It introduces a framework connecting cylindrical martingale problems with Lévy-type operators to SPDE solutions, including well-posedness and Girsanov-type formulas.

## Key findings

- Cylindrical martingale problems are equivalent to weak SPDE solutions.
- Well-posed problems have the strong Markov property.
- Existence and uniqueness of solutions are established.

## Abstract

We introduce and discuss L\'evy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic partial differential equations. Moreover, well-posed problems possess the strong Markov property and a Cameron-Martin-Girsanov-type formula holds. As applications, we derive existence and uniqueness results.