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An introduction to stochastic processes for physicists

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Stochastic Processes in Nonequilibrium Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 84))

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References

  1. Basic texts for physicists are: S. CHANDRASEKHAR, Rev. Mod. Phys. 15, 1 (1943) and M.C. WANG and G.E. UHLENBECK, Rev. Mod. Phys. 17, 323 (1945). (Both are reprinted in: N. WAX, ed., Selected Papers on Noise and Stochastic Processes, Dover, New York, 1954.) The best known textbooks are A.T. BHARUCHA-REID, Elements of the Theory of Markov Processes and Their Application (McGraw-Hill, New York, 1960), and W.A. FELLER, An Introduction to Probability Theory and its Applications (two volumes) (Wiley, New York, 1968 and 1971).

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  2. A. KOLMOGOROFF, Grundbegriffe der Wahrscheinlichkeitsrechnung. (Ergebn. Mathem. Grenzgeb. 2, no. 3, Springer, Berlin, 1933) = Foundations of Probability Theory (Chelsea, New York, 1950).

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  3. And apart from one other, rather trivial process, J.L. DOOB, Annals of Mathem. 43, 351 (1942); also reprinted in WAX, reference 1.

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  4. K. ITÔ, Proc. Imp. Acad. Tokyo 20, 519 (1944); R.E. MORTENSEN, J. Statist. Phys. 1, 271 (1969)

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  5. For a recent survey, see N.G. VAN KAMPEN, Adv. Chem. Phys. 34, 245 (I. PRIGOGINE and S.A. RICE,eds., Wiley, New York, 1976.

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  6. The standard model is due to F. SCHLOGL, Z. Physik 253, 147 (1972); see also K.H. JANSSEN, Z. Physik 270, 67 (1974) and I. MATHESON, D.F. WALLS and C. GARDINER, J. Statist. Phys. 12, 21 (1975).

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  7. R. LANDAUER, J. Statist. Phys. 13, 1 (1975).

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  8. G. NICOLIS and I. PRIGOGINE, Self-Organization in None uilibrium Systems (Wiley, Interscience, New York, 1977).

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  9. Th. W. RUIJGROK and J.A. TJON, Physica 65, 539 (1973).

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  10. H.A. KRAMERS, Physica 7, 284 (1940) = Collected Scientific Papers (North-Holland, Amsterdam 1956), p. 754. The escape rate has been explicitly calculated for special barriers by N.G. VAN KAMPEN, J. Statist. Phys. 17, 71 (1977) and M.R. PEAR and J.H. WEINER, J. Chem. Phys., to be published. For an application, see, e.g. P.G. DE GENNES, J. Statist. Phys. 12, 463 (1975).

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  11. E. PRAFSTGAARD and N.G. VAN KAMPEN, to be published.

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  12. See also U.M. TITULAER, Physica 91A, 321 (1978).

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  1. Instituut voor Theoretische Fysica der Rijksuniversiteit, University of Utrecht, Utrecht, Maliesingel 23

    N. G. van Kampen

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  1. N. G. van Kampen
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L. Garrido P. Seglar P. J. Shepherd

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© 1978 Springer-Verlag

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van Kampen, N.G. (1978). An introduction to stochastic processes for physicists. In: Garrido, L., Seglar, P., Shepherd, P.J. (eds) Stochastic Processes in Nonequilibrium Systems. Lecture Notes in Physics, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016712

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  • DOI: https://doi.org/10.1007/BFb0016712

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08942-1

  • Online ISBN: 978-3-540-35713-1

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