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Results in Mathematics

, 74:22 | Cite as

Change of Path Formula for Generalized Wiener Integral with Applications

  • Seung Jun Chang
  • Jae Gil ChoiEmail author
Article
  • 40 Downloads

Abstract

In this paper we establish a change of path formula for generalized Wiener integral which is a generalization of the change of scale formula suggested by Cameron and Storvick. We then represent the generalized analytic Feynman integral and the generalized analytic Fourier–Feynman transform via the ordinary Feynman integral. We then proceed to express the generalized analytic Feynman integral and the generalized analytic Fourier–Feynman transform as a limit of sequences of ordinary Wiener integrals.

Keywords

Wiener integral Paley–Wiener–Zygmund stochastic integral Gaussian process generalized analytic Feynman integral generalized analytic Fourier–Feynman transform 

Mathematics Subject Classification

28C20 60J65 60G15 

Notes

Acknowledgements

The authors would like to express their gratitude to the editor and the referees for their valuable comments and suggestions which have improved the original paper. The present research was conducted by the research fund of Dankook University in 2018.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsDankook UniversityCheonanKorea

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