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November 2017 Stochastic integration with respect to cylindrical Lévy processes
Adam Jakubowski, Markus Riedle
Ann. Probab. 45(6B): 4273-4306 (November 2017). DOI: 10.1214/16-AOP1164


A cylindrical Lévy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Lévy processes in Hilbert spaces. The space of admissible integrands consists of càglàd, adapted stochastic processes with values in the space of Hilbert–Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semimartingale with càdlàg trajectories.


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Adam Jakubowski. Markus Riedle. "Stochastic integration with respect to cylindrical Lévy processes." Ann. Probab. 45 (6B) 4273 - 4306, November 2017.


Received: 1 December 2015; Revised: 1 October 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838120
MathSciNet: MR3737911
Digital Object Identifier: 10.1214/16-AOP1164

Primary: 60H05
Secondary: 28C20, 60B11, 60G20

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6B • November 201