From Feynman-Kac formula to Feynman integrals via analytic continuation

Jia-An Yan

Stochastic Processes and their Applications, 1994, vol. 54, issue 2, 215-232

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] +.

Keywords: Additive; functional; Analytic; continuation; Brownian; bridge; measures; Feynman; integrals; Feynman-Kac; formula; Generalized; Kato; class; Propagator; Schrodinger; equation (search for similar items in EconPapers)
Date: 1994
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