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Sequential Gaussian Markov Integrals*

Published online by Cambridge University Press:  22 January 2016

John A. Beekman
John A. Beekman*
Affiliation:
Ball State University, Muncie, Indiana
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In [6] R.H. Cameron defined and studied a sequential Wiener integral. This was motivated by the function space integral R.P. Feynman used in [12] to give a solution to the Schröedinger equation. In [5] the present author studied sequential Gaussian Markov integrals with a positive parameter. This paper gives sufficient conditions on the integrand for such integrals to exist, when the parameter is complex. These sequential integrals are related to ordianry Gaussian Markov integrals through a Fourier transform type formula extended from [5]. We shall show that such integrals are equal to conditional Wiener integrals of suitably modified functionals.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 9 - 21
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

Footnotes

*

This research was partially supported by the National Science Foundation through grants NSF GP-7639 and NSF GP-9634.

References

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