Van Vleck-Pauli formula for Wiener integrals and Jacobi fields

  • Nobuyuki Ikeda
  • Shojiro Manabe


In this paper, we are concerned with the explicit evaluation of Wiener integrals from the viewpoint of geometry of the space of paths. Our main purpose is to emphasize the close ties between explicit expressions of Wiener integrals associated with quadratic functionals and aspects of the theory of Jacobi fields.


Critical Path Wiener Space Volterra Operator Jacobi Field Classical Path 
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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • Nobuyuki Ikeda
    • 1
  • Shojiro Manabe
    • 2
  1. 1.Department of Computer ScienceRitsumeikan UniversityKusatsu, ShigaJapan
  2. 2.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, Osaka 560Japan

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