Journal of Statistical Physics

, Volume 31, Issue 3, pp 467–483

On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process

  • C. Van Den Broeck
Articles

Abstract

It is shown that the dichotomic Markov process converges to a white shot noise (interpreted according to the Stratonovich integration rule) in the joint limit in which the average duration of one of the states goes to zero and the value at this state goes to infinity. A further limit procedure allows us to obtain Gaussian white noise from white shot noise. These results are applied to the problem of noise-induced transitions. It is shown that white shot noise can give rise to transitions which do not occur for Gaussian white noise. The above results are finally generalized in introducing compound dichotomic Markov processes.

Key words

Dichotomic Markov process white shot noise noise-induced transitions 

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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • C. Van Den Broeck
    • 1
    • 2
  1. 1.Departement NatuurkundeVrije Universiteit BrusselBrusselBelgium
  2. 2.Aspirant NFWO BelgiumBelgium

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