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Large time behavior in random multiplicative processes

Probability 2010-07-07 v1 Mathematical Physics math.MP

Abstract

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the divergence of the fractional order moments of the solution below respectively above some critical exponent. This exponent is computed. In particular models it is the heavy tail exponent. When the equation is linear this exponent determines a new family of weak topologies (stronger compared to the classical one), related to the convergence to the stationary state.

Keywords

Cite

@article{arxiv.1007.0952,
  title  = {Large time behavior in random multiplicative processes},
  author = {Gyorgy Steinbrecher and Xavier Garbet and Boris Weyssow},
  journal= {arXiv preprint arXiv:1007.0952},
  year   = {2010}
}

Comments

20 pages

R2 v1 2026-06-21T15:45:05.501Z