Abstract
A Fokker-Planck equation was first used by Fokker [1.1] and Planck [1.2] to describe the Brownian motion of particles. To become familiar with this equation we first discuss the Brownian motion of particles in its simplest form.
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References
A. D. Fokker: Ann. Physik 43, 810 (1914)
M. Planck: Sitzber. Preuß. Akad. Wiss. p. 324 (1917)
P. Langevin: Comptes rendus 146, 530 (1908)
A. Einstein: Ann. Physik 17, 549 (1905) and 19, 371 (1906)
G. E. Uhlenbeck, L. S. Ornstein: Phys. Rev. 36, 823 (1930)
S. Chandrasekhar: Rev. Mod. Phys. 15, 1 (1943)
M. C. Wang, G. E. Uhlenbeck: Rev. Mod. Phys. 17, 323 (1945)
References [1.5 – 7] and other articles are contained in: N. Wax (ed.): Selected Papers on Noise and Stochastic Processes (Dover, New York 1954)
A. T. Bharucha-Reid: Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, New York 1960)
R. L. Stratonovich: Topics in the Theory of Random Noise, Vols. I and II (Gordon & Breach, New York 1963 and 1967)
M. Lax: Rev. Mod. Phys. 32, 25 (1960)
(a), 38, 359 (1966)
(b) and 38, 541 (1966) (c)
N. S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic, New York 1974)
H. Haken: Rev. Mod. Phys. 47, 67 (1975)
H. Haken: Synergetics, An Introduction, 3rd ed. Springer Ser. Synergetics, Vol. 1 (Springer, Berlin, Heidelberg, New York 1983)
Z. Schuss: Theory and Applications of Stochastic Differential Equations (Wiley, New York 1980)
O. Klein: Arkiv for Mathematik, Astronomi, och Fysik 16, No 5 (1921)
H. A. Kramers: Physica 7, 284 (1940)
M. v. Smoluchowski: Ann. Physik 48, 1103 (1915)
J. E. Moyal: J. Roy. Stat. Soc. (London) B 11, 150 (1949)
L. Boltzmann: Lectures on Gas Theory, transl. by S. Brush (University of California Press, Berkley 1964)
R. Balescu: Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York 1975) Chap. 11
P. Résibois, M. De Leener: Classical Kinetic Theory of Fluids (Wiley, New York 1977) Chap. 9
P. L. Bhatnagar, E. P. Gross, M. Krook: Phys. Rev. 94, 511 (1954)
N. G. van Kampen: Adv. Chem. Phys. 34, 245 (1976)
I. Prigogine, P. Résibois: Physica 24, 795 (1958)
S. Nakajima: Prog. Theor. Phys. 20, 948 (1958)
R. W. Zwanzig: J. Chem. Phys. 33, 1338 (1960)
F. Haake: Springer Tracts Mod. Phys. 66, 98 (Springer, Berlin, Heidelberg, New York 1973)
V. M. Kenkre: In Statistical Mechanics and Statistical Methods in Theory and Applications, ed. by U. Landmann (Plenum, New York 1977) p. 441
H. Grabert: Springer Tracts Mod. Phys. 95 (Springer, Berlin, Heidelberg, New York 1982)
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Risken, H. (1984). Introduction. In: The Fokker-Planck Equation. Springer Series in Synergetics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96807-5_1
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