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

Mhelmar A‎. ‎Labendia

doi:10.15352/aot.1810-1435

Abstract

‎ ‎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.

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Mhelmar A‎. ‎Labendia. "A Riemann-type definition of the Itô integral for the operator-valued stochastic process." Adv. Oper. Theory 4 (3) 625 - 640, Summer 2019. https://doi.org/10.15352/aot.1810-1435

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Received: 30 October 2018; Accepted: 9 January 2019; Published: Summer 2019

First available in Project Euclid: 2 March 2019

zbMATH: 07056789

MathSciNet: MR3919035

Digital Object Identifier: 10.15352/aot.1810-1435

Subjects:

Primary: 60H30

Secondary: 60H05

Keywords: ‎$Q$-Wiener process‎ , ‎belated McShane integrable‎ , classical Itô integral , Itô-McShane integrable‎‎

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