The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral
Abstract
A numerical simulation algorithm that is exact for any time step \ensuremath{\Delta}t>0 is derived for the Ornstein-Uhlenbeck process X(t) and its time integral Y(t). The algorithm allows one to make efficient, unapproximated simulations of, for instance, the velocity and position components of a particle undergoing Brownian motion, and the electric current and transported charge in a simple R-L circuit, provided appropriate values are assigned to the Ornstein-Uhlenbeck relaxation time \ensuremath{\tau} and diffusion constant c. A simple Taylor expansion in \ensuremath{\Delta}t of the exact simulation formulas shows how the first-order simulation formulas, which are implicit in the Langevin equation for X(t) and the defining equation for Y(t), are modified in second order. The exact simulation algorithm is used here to illustrate the zero-\ensuremath{\tau} limit theorem. \textcopyright{} 1996 The American Physical Society.
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Cites
Stochastic Problems in Physics and Astronomy
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On the Theory of the Brownian Motion
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Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
Gardiner, C. W. (1985) · Springer Series in Synergetics · doi:10.1007/978-3-662-02452-2 · Cited by 3,703
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Zur Theorie der Brownschen Bewegung
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Metadata
- Authors
- Gillespie, D. T.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1996-08-01
- Volume
- 54
- Issue
- 2
- Pages
- 2084-2091
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1997461667
- Cited by
- 566
- References
- 12
- FWCI
- 1.80
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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