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

Mhelmar A‎. ‎Labendia

#### 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.

#### Article information

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

Dates
Accepted: 9 January 2019
First available in Project Euclid: 2 March 2019

https://projecteuclid.org/euclid.aot/1551495624

Digital Object Identifier
doi:10.15352/aot.1810-1435

Mathematical Reviews number (MathSciNet)
MR3919035

Zentralblatt MATH identifier
07056789

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

#### Citation

‎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. https://projecteuclid.org/euclid.aot/1551495624

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