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September 1996 Laplace and the origin of the Ornstein-Uhlenbeck process
Martin Jacobsen
Bernoulli 2(3): 271-286 (September 1996). DOI: 10.3150/bj/1178291723


It is shown that a second-order partial differential equation, found by Laplace in 1810, is the Fokker-Planck equation for a one-dimensional Ornstein-Uhlenbeck process. It is argued that Laplace's reasoning, although not rigorous, can be entirely justified by using the modern theory of weak convergence of stochastic processes. The solutions to the differential equation found by Laplace and others, using expansions in terms of Hermite polynomials, are discussed.


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Martin Jacobsen. "Laplace and the origin of the Ornstein-Uhlenbeck process." Bernoulli 2 (3) 271 - 286, September 1996.


Published: September 1996
First available in Project Euclid: 4 May 2007

zbMATH: 0965.60067
MathSciNet: MR1416867
Digital Object Identifier: 10.3150/bj/1178291723

Keywords: Bernoulli-Laplace urn model , diffusion process , Fokker-Planck equation , Hermite polynomials , weak convergence

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability


Vol.2 • No. 3 • September 1996
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