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

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

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
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. 

References

Cameron, R. H. and Graves, G. E., ‘Additional functionals on a space of continuous functions, I’, Trans. Amer. Math. Soc. 70 (1951), 160–176.CrossRefGoogle Scholar
Cameron, R. H. and Martin, W. T., ‘Transformations of Wiener integrals under translations’, Ann. of Math. (2) 45 (1944), 386–396.CrossRefGoogle Scholar
Cameron, R. H. and Storvick, D. A., ‘Some Banach algebras of analytic Feynman integrable functionals’, in: Analytic Functions (Kozubnik, 1979), Lecture Notes in Mathematics, 798 (ed. Ławrynowicz, J.) (Springer, Berlin, 1980), 18–67.CrossRefGoogle Scholar
Cameron, R. H. and Storvick, D. A., ‘A new translation theorem for the analytic Feynman integral’, Rev. Roumaine Math. Pures Appl. 27 (1982), 937–944.Google Scholar
Chang, S. J., Choi, J. G. and Skoug, D., ‘Integration by parts formulas involving generalized Fourier–Feynman transforms on function space’, Trans. Amer. Math. Soc. 355 (2003), 2925–2948.CrossRefGoogle Scholar
Chang, S. J. and Chung, D. M., ‘Conditional function space integrals with applications’, Rocky Mountain J. Math. 26 (1996), 37–62.CrossRefGoogle Scholar
Chang, S. J. and Skoug, D., ‘Generalized Fourier–Feynman transforms and a first variation on function space’, Integral Transforms Spec. Funct. 14 (2003), 375–393.CrossRefGoogle Scholar
Choi, J. G., Chung, H. S. and Chang, S. J., ‘Sequential generalized transforms on function space’, Abstr. Appl. Anal. 2013 (2013), 565832, 12 pages.CrossRefGoogle Scholar
Choi, J. G., Skoug, D. and Chang, S. J., ‘Generalized analytic Fourier–Feynman transform of functionals in a Banach algebra FA 1, A 2a, b’, J. Funct. Spaces Appl. 2013 (2013), 954098, 12 pages.CrossRefGoogle Scholar
Yeh, J., ‘Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments’, Illinois J. Math. 15 (1971), 37–46.CrossRefGoogle Scholar
Yeh, J., Stochastic Processes and the Wiener Integral (Marcel Dekker, New York, 1973).Google Scholar