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Toru Sera

Publications and source records attributed to Toru Sera.

10 recordsLinked to original sources
arXiv2025

Large deviations related to Dynkin--Lamperti arcsine laws for last visit times of Markov processes

We establish large deviation estimates related to the Dynkin--Lamperti arcsine laws for subordinators whose Laplace exponents are either regularly varying or comparable to regularly varying functions. By applying these results to inverse local times, we derive large deviation estimates for the last visit times to the starting point of various Hunt processes satisfying suitable on-diagonal resolvent density estimates, such as one-dimensional generalized diffusion processes, one-dimensional L\'evy processes, and Brownian motion and its subordinate process on the Sierpi\'nski gasket.

math.PR↗
arXiv2024

Higher order approximations in arcsine laws for subordinators

We establish higher order approximations in the Dynkin--Lamperti theorem, a limit theorem for the distribution of a killed subordinator immediately before its first passage time over a fixed level. For this purpose, we also study asymptotic expansions of potential densities for killed subordinators.

math.PR↗
arXiv2024

Large deviations for occupation and waiting times of infinite ergodic transformations

We establish large deviation estimates related to the Darling--Kac theorem and generalized arcsine laws for occupation and waiting times of ergodic transformations preserving an infinite measure, such as non-uniformly expanding interval maps with indifferent fixed points. For the proof, we imitate the study of generalized arcsine laws for occupation times of one-dimensional diffusion processes and adopt a method of double Laplace transform.

math.DS↗
arXiv2023

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

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 [S\'eminaire de Probabilit\'es 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.

math.DS↗
arXiv2020

Aging arcsine law in Brownian motion and its generalization

Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes.

math.PR↗
arXiv2019

Tied-down occupation times of infinite ergodic transformations

We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting random variables include the local times of $p$-stable L\'evy-bridges ($1<p\le 2$) and the transformations involved exhibit "tied-down renewal mixing" properties which refine rational weak mixing. Periodic local limit theorems for Gibbs-Markov and AFU maps are also established.

math.DS↗
arXiv2019

Functional limit theorem for occupation time processes of intermittent maps

We establish a functional limit theorem for the joint-law of occupations near and away from indifferent fixed points of interval maps, and of waits for the occupations away from these points, in the sense of strong distributional convergence. It is a functional and joint-distributional extension of Darling--Kac type limit theorem, of Lamperti type generalized arcsine laws for occupation times, and of Dynkin and Lamperti type generalized arcsine laws for waiting times, at the same time.

math.PR↗
arXiv2018

Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations

We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges to a multidimensional version of Lamperti's generalized arcsine distribution, in the sense of strong distributional convergence. Our results can be applied to interval maps and Markov chains. We adopt the double Laplace transform method, which has been utilized in the study of occupation times of diffusions on multiray. We also discuss the inverse problem.

math.PR↗