Generalized uniform laws for tied-down occupation times of infinite ergodic transformations

2023/08/18 by Aaronson, Jon., Sera, Toru
#60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37A40 #Probability (math.PR) #Secondary 37A50

paper · doi:10.48550/arxiv.2308.09406

Abstract

We establish a conditional limit theorem for occupation times of infinite ergodic transformations under a tied-down condition, that is, the condition that the orbit returns to a reference set with finite measure at the final observation time. The class of limit distributions is the generalization of the uniform distribution which was discovered by M. Barlow, J. Pitman and M. Yor in [Séminaire de Probabilités XXIII. Lecture Notes in Mathematics, volume 1372 (1989), 294--314]. For the proof we utilize operator renewal theory. Our result can be applied to intermittent maps with two or more indifferent fixed points.

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