content_image/364343.jpg content_image/364344.jpg content_image/364345.jpg content_image/364346.jpg content_image/364347.jpg content_image/364348.jpg content_image/364349.jpg content_image/364350.jpg
## C. α ∈ (1 , 2) 

Since in this case lim$_{t}$ →∞ 〈 Y$_{t}$ 〉 $^{2}$/ 〈 Y 2 t 〉 = 1 (see below), for finding the long-time behavior of σ $^{2}$( t ) we should determine the first two terms of the asymptotic expansion of 〈 Y$_{t}$ 〉 and 〈 Y 2 t 〉 as t → ∞ . To this end, taking into account that at α ∈ (1 , 2) the mean waiting time τ = ∫ ∞ τ$_{min}$ dτ τ p ( τ ) exists, we use the following formula: ∞ − 

Proceeding in the same way as before, we obtain 

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as s → 0, and the straightforward calculation of the Laplace transforms (4.8) yields 

and 

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These asymptotic formulas are particular cases of the asymptotic formula (4.3) with L (1 /s ) = const. Therefore, using the well-known property of the gamma function, Γ(1+ x ) = x Γ( x ), from (4.4) we get 

and 

as t → ∞ . Accordingly, the long-time behavior of the variance σ $^{2}$( t ) is described by the power law 

Thus, since α ∈ (1 , 2), the transport of particles is superdiffusive. Interestingly, depending on the exponent α , the increase of the particle mass µ can either enhance or suppress the biased diffusion. In order to show this, we first use Eq. (3.1) with m = 1 to represent the mean waiting time τ in the form 

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