@article{
 title = {Stationary states in single-well potentials under symmetric Lévy noises},
 type = {article},
 year = {2010},
 keywords = {Stationary states,Stochastic particle dynamics (theory),Stochastic processes (theory)},
 volume = {2010},
 id = {2e640f20-b9b3-31ce-b030-2e660e73ae3d},
 created = {2020-10-30T10:12:16.602Z},
 file_attached = {false},
 profile_id = {f5390430-7317-381a-8c56-e25a878d78ef},
 last_modified = {2020-10-30T10:12:16.602Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {We discuss the existence of stationary states for subharmonic potentials V(x) ∝ |x|c, c < 2, under the action of symmetric α-stable noises. We show analytically that the necessary condition for the existence of the steady state is c > 2 - α. Consequently, for harmonic (c = 2) and superharmonic potentials (c > 2) driven by any α-stable noise, steady states always exist. Stationary states are characterized by probability density functions P(x) ∝ x-(c+α-1) for |x| → ∞ having a lighter tail than the noise distribution for superharmonic potentials (c > 2) and a heavier tail than the noise distribution for subharmonic ones. Monte Carlo simulations confirm the existence of such stationary states and the form of the tails of the corresponding probability densities. © 2010 IOP Publishing Ltd and SISSA.},
 bibtype = {article},
 author = {Dybiec, B. and Sokolov, I.M. and Chechkin, A.V.},
 doi = {10.1088/1742-5468/2010/07/P07008},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 number = {7}
}

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