Stochastic integration with respect to cylindrical Lévy processes by p-summing operators

Tomasz Andrzej Kosmala; Markus Riedle

doi:10.1007/s10959-019-00978-x

Stochastic integration with respect to cylindrical Lévy processes by p-summing operators

Tomasz Andrzej Kosmala, Markus Riedle

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4 Citations (Scopus)

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Abstract

We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for 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.

Original language	English
Journal	JOURNAL OF THEORETICAL PROBABILITY
Early online date	4 Jan 2020
DOIs	https://doi.org/10.1007/s10959-019-00978-x
Publication status	E-pub ahead of print - 4 Jan 2020

Keywords

cylindrical Lévy processes
stochastic integration in Banach spaces
stochastic partial differential equations
p-summing operators
Cylindrical Lévy processes
Stochastic partial differential equations
p-Summing operators
Stochastic integration in Banach spaces

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10.1007/s10959-019-00978-x

Stochastic Integration with Respect_KOSMALA_Accepted9December2019_Published4January2020_GOLD VoR (CC BY)Final published version, 377 KBLicence: CC BY

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abstract = "We introduce a stochastic integral with respect to cylindrical L{\'e}vy processes with finite p-th weak moment for 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 L{\'e}vy process.",

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author = "Kosmala, {Tomasz Andrzej} and Markus Riedle",

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doi = "10.1007/s10959-019-00978-x",

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AU - Kosmala, Tomasz Andrzej

AU - Riedle, Markus

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N2 - We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for 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.

AB - We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for 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.

KW - cylindrical Lévy processes

KW - stochastic integration in Banach spaces

KW - stochastic partial differential equations

KW - p-summing operators

KW - Cylindrical Lévy processes

KW - Stochastic partial differential equations

KW - p-Summing operators

KW - Stochastic integration in Banach spaces

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JO - JOURNAL OF THEORETICAL PROBABILITY

JF - JOURNAL OF THEORETICAL PROBABILITY

ER -

Stochastic integration with respect to cylindrical Lévy processes by p-summing operators

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