## The Annals of Probability

### Stochastic integration with respect to cylindrical Lévy processes

#### Abstract

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.

#### Article information

Source
Ann. Probab. Volume 45, Number 6B (2017), 4273-4306.

Dates
Revised: October 2016
First available in Project Euclid: 12 December 2017

https://projecteuclid.org/euclid.aop/1513069260

Digital Object Identifier
doi:10.1214/16-AOP1164

#### Citation

Jakubowski, Adam; Riedle, Markus. Stochastic integration with respect to cylindrical Lévy processes. Ann. Probab. 45 (2017), no. 6B, 4273--4306. doi:10.1214/16-AOP1164. https://projecteuclid.org/euclid.aop/1513069260

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