Stochastic Differential Equations

  • P. Zoller
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)


This is a brief introduction to Langevin equations (stochastic differential equations (SDE) with white noise terms)[1–3], with particular emphasis on its use as a calculational tool. We also discuss recently developed (matrix) continued fraction methods for solving certain types of stochastic differential equations and their associated Fokker-Planck equation [4–6].


Stochastic Differential Equation Wiener Process Langevin Equation Fokker Planck Equation Stochastic Differential Equation 


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  1. 1.
    L. Arnold, Stochastic Differential Equations (Wiley-Interscience, New York, 1974).MATHGoogle Scholar
  2. 2.
    I.I. Grihman and A.V. Skorokod, Stochastic Differential Equations (Springer, Berlin, Heidelberg, New York, 1972).Google Scholar
  3. 3.
    C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, Heidelberg, New York, Tokyo, 1983); and unpublished lecture notes.MATHGoogle Scholar
  4. 4.
    H. Risken, The Fokker-Planck-Equation (Springer, in press).Google Scholar
  5. 5.
    P. Zoller, G. Alber and R. Salvador, Phys. Rev. A 24 (1981) 398; P. Zoller and J. Cooper, Phys. Rev. A 28 (1983) 2310.CrossRefADSGoogle Scholar
  6. 6.
    K. Wodkiewicz, J. Math. Phys. 23(1982) 2179.CrossRefMATHADSMathSciNetGoogle Scholar
  7. 7.
    P.D. Drummond, C.W. Gardiner and D.F. Walls, Phys. Rev. A 24 (1981) 914.CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    H. Haken, Synergetics, An Introduction (Springer, Berlin, Heidelberg, New York, 1978).MATHGoogle Scholar
  9. 9.
    H. Haken, Laser Theory, Encyclopedia of Physics XXV/2c, eds. S. Flügge and L. Genzel (Springer, New York, 1970).Google Scholar
  10. 10.
    J.M. Sancho, M. San Miguel, S.L. Katz and J.D. Gunton, Phys. Rev. A (1982) 1589,and references cited.Google Scholar
  11. 11.
    H.G. Van Kampen, Stochastic Process in Physics and Chemistry (North-Holland, Amsterdam, 1981).Google Scholar
  12. 12.
    H. Denk and M. Riederle, J. Approx. Theory 35 (1982) 355,and references cited.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    D.F. Walls, Nature 280 (1979) 451.CrossRefADSGoogle Scholar
  14. 14.
    D.F. Walls, Nature, in press.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • P. Zoller
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of InnsbruckInnsbruckAustria

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