Stochastic integration with respect to cylindrical L\'evy processes by p-summing operators

TL;DR

This paper develops a new stochastic integration framework for cylindrical Lévy processes using p-summing operators, enabling the analysis of stochastic evolution equations in Banach spaces.

Contribution

It introduces a novel stochastic integral with respect to cylindrical Lévy processes using p-summing operators, expanding the tools for stochastic analysis in Banach spaces.

Findings

Established existence of solutions for stochastic evolution equations driven by cylindrical Lévy processes.

Developed a stochastic integration theory for processes with finite p-th weak moments.

Applied the theory to solve specific stochastic evolution equations.

Abstract

We introduce a stochastic integral with respect to cylindrical L\'evy processes with finite $p$-th weak moment for $p\in [1,2]$. The space of integrands consists of $p$-summing operators between Banach spaces of martingale type $p$. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical L\'evy process.