An extension of Wiener integration with the use of operator theory

Palle E.T Jorgensen; Myung Sin Song

doi:10.1063/1.3196622

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An extension of Wiener integration with the use of operator theory

Journal article

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An extension of Wiener integration with the use of operator theory

Palle E.T Jorgensen and Myung Sin Song

Journal of Mathematical Physics, Vol.50(10), pp.103502-103502-11

2009

DOI: 10.1063/1.3196622

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Abstract

With the use of tensor product of Hilbert space and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.

Details

Title: Subtitle: An extension of Wiener integration with the use of operator theory
Creators: Palle E.T Jorgensen
Myung Sin Song
Resource Type: Journal article
Publication Details: Journal of Mathematical Physics, Vol.50(10), pp.103502-103502-11
DOI: 10.1063/1.3196622
ISSN: 0022-2488
eISSN: 1089-7658
Language: English
Date published: 2009
Academic Unit: Mathematics
Record Identifier: 9983985998402771

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