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On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process. (English) Zbl 0588.60081
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.

MSC:
60J70Applications of Brownian motions and diffusion theory
60H10Stochastic ordinary differential equations
60K35Interacting random processes; statistical mechanics type models; percolation theory
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Full Text: DOI
References:
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