Limit theorems for continuous-time random walks with infinite mean waiting times
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...…the special case µ = 1/2 reveals the FPTD a(πx0)−1/2 exp(−a2t2/(4x0)) where a is the amplitude of the Lévy stable law, and x0 is the distance of the absorbing barrier from the initial location (Eliazar and Klafter 2004); compare also to the detailed discussion in Meerschaert and Scheffler 2004....
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"Limit theorems for continuous-time ..." refers background in this paper
...Then b(t) = t−1/βL(t) for some slowly varying function L(t) (so that L(λt)/L(t) → 1 as t → ∞ for any λ > 0, see for example [14]) and it follows from Example 11....
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...If {A(t)} is an operator Lévy motion on R and if ν is the probability distribution of A(t) then the linear operators Ttf(x) = ∫ f(x − y)ν(dy) form a convolution semigroup [14, 16] with generator L = limt↓0 t (Tt − T0)....
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