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A TRANSLATION THEOREM FOR THE GENERALISED ANALYTIC FEYNMAN INTEGRAL ASSOCIATED WITH GAUSSIAN PATHS

Part of: Markov processes Set functions and measures on spaces with additional structure Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 September 2015

SEUNG JUN CHANG ,
JAE GIL CHOI  and
AE YOUNG KO
SEUNG JUN CHANG
Affiliation:
Department of Mathematics, Dankook University, Cheonan 330-714, Republic of Korea email sejchang@dankook.ac.kr
JAE GIL CHOI*
Affiliation:
Department of Mathematics, Dankook University, Cheonan 330-714, Republic of Korea email jgchoi@dankook.ac.kr
AE YOUNG KO
Affiliation:
Department of Mathematics, Dankook University, Cheonan 330-714, Republic of Korea email ayko@dankook.ac.kr
*
✉jgchoi@dankook.ac.kr
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Abstract

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In this paper, we establish a translation theorem for the generalised analytic Feynman integral of functionals that belong to the Banach algebra ${\mathcal{F}}(C_{a,b}[0,T])$.

Keywords

generalised Brownian motion processGaussian processgeneralised analytic Feynman integralFresnel-type classtranslation theorem

MSC classification

Primary: 60J65: Brownian motion
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) 46G12: Measures and integration on abstract linear spaces

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 152 - 161
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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