Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 54, Issue 2, 1996, Pages 2084-2091

  Gillespie, Daniel T ^a  

^a NAVAL AIR WARFARE CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001247687     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.54.2084     Document Type: Article

References (19)

1. P. Langevin, Comptes Rendues146, 530 (1908).
2. G E. Uhlenbeck and L S. Ornstein, Phys. Rev.36, 823 (1930).
3. S. Chandrasekhar, Rev. Mod. Phys.15, 1 (1943).
4. Ming Chen Wang and G E. Uhlenbeck, Rev. Mod. Phys.17, 323 (1945).
5. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), Chap. 15.
6. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
7. C W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer-Verlag, Berlin, 1985).
8. D T. Gillespie, Markov Processes: An Introduction for Physical Scientists (Academic, New York, 1992).
9. D T. Gillespie, Am. J. Phys.64, 225 (1996).
10. A few of the many recent papers to employ the OU process as a 'colored noise' source are as follows: J. Müller and J. Schnakenberg, Ann. Phys. (Leipzig)2, 92 (1993);
11. J. Luczka, P. Hänggi and A. Gadomski, Phys. Rev. E51, 2933 (1995);
12. M. Wu, K. Billah and M. Shinozuka, Phys. Rev. E52, 3377 (1995);
13. P. Reimann, Phys. Rev. E52, 1579 (1995);
14. and F. Castro, A. Sánchez and H. Wio, Phys. Rev. Lett.75, 1691 (1995).
15. A pedagogical discussion of the non-Markovian nature of Y, and the bivariate Markovian nature of (X,Y), may be found in D. T. Gillespie, Am. J. Phys. (to be published).
16. To the best of this author's knowledge, the earliest published appearance of the exact OU updating formula (1.10) occurs in Ref. 8 at Eq. (E-12b). Later appearances occur in N J. Kasdin, Proc. IEEE83, 802 (1995) at Eqs. (56) and (57), and also in Ref. 9 at Eq. (2.47).
17. A. Einstein, Ann. Phys. (Leipzig)17, 549 (1905);
18. A. Einstein, Ann. Phys. (Leipzig)19, 371 (1906).
19. See also Ref. 7, pp.2–6.