Distributional limit theorems in infinite ergodic theory

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L\'evy walks (2014, background): “The concept of infinite measure (Aaronson, 1997; Thaler and Zweimüller, 2006) provides with such theoretical framework (Rebenshtok et al., 2014a,b).”
Mixing Limit Theorems for Ergodic Transformations (2007, methodology): “... an infinite measure μ): For a fixed set Y ∈ A, μ(Y ) > 0, we define the N0-valued variables Zn(Y ), n ≥ 0, on X by Zn(Y )(x) := max({0 }∪{ 1 ≤ k ≤ n : T k x ∈ Y }), which gives the time of the last visit to Y up to time n. The Dynkin-Lamperti arcsine law for waiting times describes the asymptoti”
Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, background): “See also [39, 41] for more general transformations.”