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Exact computation of Feynman-type integrals involving Gaussian random fields (2000)

Kallianpur, G. ; Papanicolaou, V. G.

Springer

Stochastic environmental research and risk assessment 14 (2000), S. 33-49

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ISSN: 1436-3259

Keywords: Key words: Feynman integral, multiparameter Gaussian (or Wiener) process, Brownian sheet/tent.

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s004770050003

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