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We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of neutral fixed points.
Roland Zweimüller. "Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps." Fundamenta Mathematicae 198.2 (2008): 125-138. <http://eudml.org/doc/282977>.
@article{RolandZweimüller2008, abstract = {We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of neutral fixed points.}, author = {Roland Zweimüller}, journal = {Fundamenta Mathematicae}, keywords = {infinite invariant measure; limit distribution; hitting times; indifferent fixed points}, language = {eng}, number = {2}, pages = {125-138}, title = {Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps}, url = {http://eudml.org/doc/282977}, volume = {198}, year = {2008}, }
TY - JOUR AU - Roland Zweimüller TI - Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps JO - Fundamenta Mathematicae PY - 2008 VL - 198 IS - 2 SP - 125 EP - 138 AB - We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of neutral fixed points. LA - eng KW - infinite invariant measure; limit distribution; hitting times; indifferent fixed points UR - http://eudml.org/doc/282977 ER -