Asymptotic behaviour for critical slowing-down random walks
نویسنده
چکیده
The jump processes W (t) on [0,∞[ with transitions w → αw at rate bwβ (0 ≤ α ≤ 1, b > 0, β > 0) are considered. Their moments are shown to decay not faster than algebraically for t → ∞, and an equilibrium probability density is found for a rescaled process U = (t + κ)−βW . A corresponding birth process is discussed. PACS numbers: 02.50.Ey Stochastic processes 05.20.Dd Kinetic theory 83.70.Fn Granular solids 05.40.Fb Random walks and Levy flights AMS 1991 MSC : 60C18 Self-similar stochastic processes 82C23 Exactly solvable dynamic models (time-dependent statistical physics) 70F35 Collisions
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