Toru Sera
YOU?
Author Swipe
View article: Large deviations for occupation and waiting times of infinite ergodic transformations
Large deviations for occupation and waiting times of infinite ergodic transformations Open
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 map…
View article: Higher order approximations in arcsine laws for subordinators
Higher order approximations in arcsine laws for subordinators Open
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 asymptoti…
View article: Large deviations for occupation and waiting times of infinite ergodic transformations
Large deviations for occupation and waiting times of infinite ergodic transformations Open
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 ma…
View article: Generalized uniform laws for tied-down occupation times of infinite ergodic transformations
Generalized uniform laws for tied-down occupation times of infinite ergodic transformations Open
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 ti…
View article: Functional limits for "tied down" occupation time processes of infinite ergodic transformations
Functional limits for "tied down" occupation time processes of infinite ergodic transformations Open
We prove functional, distributional limit theorems for the occupation times of pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting processes are tied down Mittag-Leffler processes and th…
View article: Aging arcsine law in Brownian motion and its generalization
Aging arcsine law in Brownian motion and its generalization Open
Classical arcsine law states that the 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 pre…
View article: Resolution of sigma-fields for multiparticle finite-state action evolutions with infinite past
Resolution of sigma-fields for multiparticle finite-state action evolutions with infinite past Open
For multiparticle finite-state action evolutions, we prove that the observation $ σ$-field admits a resolution involving a third noise which is generated by a random variable with uniform law. The Rees decomposition from the semigroup theo…
View article: Tied-down occupation times of infinite ergodic transformations
Tied-down occupation times of infinite ergodic transformations Open
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 variable…
View article: Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations Open
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 di…
View article: Functional limit theorem for occupation time processes of infinite ergodic transformations
Functional limit theorem for occupation time processes of infinite ergodic transformations Open
We establish a functional limit theorem for joint laws of occupation time processes of infinite ergodic transformations, in the sense of strong distributional convergence. Our limit theorem is a functional and joint-distributional extentio…
View article: Functional limit theorem for occupation time processes of intermittent maps
Functional limit theorem for occupation time processes of intermittent maps Open
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 convergen…
View article: Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations Open
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 di…