# Stochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space

## TL;DR

This paper develops a new framework for stochastic integration and SPDEs driven by jumps in the dual of a nuclear space, enabling analysis of complex Lévy-driven systems.

## Contribution

It introduces a novel theory of stochastic integration for cylindrical martingale measures in nuclear space duals, extending SPDE analysis to Lévy processes.

## Key findings

- Established a weak and strong stochastic integration framework
- Applied the theory to SPDEs with general coefficients
- Enabled analysis of Lévy process-driven SPDEs

## Abstract

We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to develop a theory of SPDEs with rather general coefficients. In particular, we can then study SPDEs driven by general L\'{e}vy processes in this context.