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

Tomasz Kosmala () and Markus Riedle ()
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Tomasz Kosmala: King’s College London
Markus Riedle: King’s College London

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 477-497

Abstract: Abstract We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$ p ∈ [ 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 Lévy process.

Keywords: Cylindrical Lévy processes; Stochastic integration in Banach spaces; Stochastic partial differential equations; p-Summing operators; 47B10; 60G51; 46T12; 60H15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00978-x

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