Stochastic integration with respect to canonical α-stable cylindrical Lévy processes

In this work, we introduce a theory of stochastic integration with respect to symmetric α-stable cylindrical Lévy processes. Since processes do not enjoy semi-martingale decomposition, our approach is based on decoupling inequality for the tangent sequence Radonified increments. This enables us characterise largest space predictable Hilbert-Schmidt operator-valued which are integrable an process as collection all paths in Bochner Lα. We demonstrate power and robustness developed by establishing dominated convergence result allowing interchange integral limit.