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From Feynman-Kac formula to Feynman integrals via analytic continuation

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  • Yan, Jia-An

Abstract

By using a calculus based on Brownian bridge measures, it is shown that under mild assumptions on V (e.g. V is in the Kato class) the fundamental solution (FS) q (t,x,y) for the heat equation can be represented by the Feynman-Kac formula. Furthermore, it has an analytic continuation in t over +, where , and q([var epsilon] + it,x,y) can be expressed via Wiener path integrals. For small [var epsilon] > 0 it can be considered as an approximation of the FS for the Schrodinger equation . We also give an estimate of q(t,x,y) for t [set membership, variant] +.

Suggested Citation

  • Yan, Jia-An, 1994. "From Feynman-Kac formula to Feynman integrals via analytic continuation," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 215-232, December.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:2:p:215-232
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    Cited by:

    1. Luo, S. L. & Yan, J. A., 1999. "A complex scaling approach to sequential Feynman integrals," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 287-300, February.

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