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Exact computation of Feynman-type integrals involving Gaussian random fields |
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| Authors: | G Kallianpur V G Papanicolaou |
| Institution: | (1) Department of Statistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260, USA, US;(2) Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67206-0033, USA, US;(3) Department of Mathematics, National Technical University of Athens, Zografou 157 80, Greece, GR |
| Abstract: | We calculate explicitly some expectations (integrals over Hilbert spaces) of functionals of Gaussian random fields. Our work is inspired by the formulas for the harmonic oscillator. We also show how to do similar calculations by considering continuum limits of sequences of coupled harmonic oscillators. The results obtained in this work have applications in the study of random media, renormalization and scaling, and in engineering perturbation analysis. |
| Keywords: | : Feynman integral multiparameter Gaussian (or Wiener) process Brownian sheet/tent |
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