Asymptotic behaviour for critical slowing-down random walks
Abstract
The jump processes W(t) on [0,∞[ with transitions w -> alpha w at rate b*wbeta (0 =< alpha =< 1, b>0, beta>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 + k)-beta W. A corresponding birth process is discussed.
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