Advances in Operator Theory

A Riemann-type definition of the Itô integral for the operator-valued stochastic process

Mhelmar A‎. ‎Labendia

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‎ ‎In this paper‎, ‎we introduce the Itô-McShane integral and show that the classical Itô integral of an operator-valued stochastic process with respect to a Hilbert space-valued $Q$-Wiener process can be defined‎, ‎using the Itô-McShane integral‎.

Article information

Adv. Oper. Theory, Volume 4, Number 3 (2019), 625-640.

Received: 30 October 2018
Accepted: 9 January 2019
First available in Project Euclid: 2 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H05: Stochastic integrals

Itô-McShane integrable‎‎ ‎belated McShane integrable‎ classical Itô integral $Q$-Wiener process


‎Labendia, Mhelmar A‎. A Riemann-type definition of the Itô integral for the operator-valued stochastic process. Adv. Oper. Theory 4 (2019), no. 3, 625--640. doi:10.15352/aot.1810-1435.

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