Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for p∈[1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\in [1,2]$$\end{document}. 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 Lévy process.