Ornstein-Uhlenbeck Path Integral and Its Application

Hiroshi Ezawa
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Hiroshi Ezawa: Gakushuin University, Department of Physics

A chapter in Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, 2001, pp 119-135 from Springer

Abstract: Abstract Introducing a path integral for the Ornstein-Uhlenbeck process distorted by a potential V(x), we find out the T → ∞ limit of the probability distributions of X[ω] := 1/T ν ∫ 0 T V(ω(t)) dt for Ornstein-Uhlenbeck process ω(t), with appropriate values of the exponent ν that depend on V. The results are compared with those for the Wiener process.

Keywords: 47D08; 60K40; Ornstein-Uhlenbeck process; Wiener process; Feynman-Kac formula; long-time average (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0842-6_7

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DOI: 10.1007/978-94-010-0842-6_7

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