Large deviation estimates related to arcsine laws for subordinators

2025/11/10 by Sera, Toru
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Primary 60G51 #Probability (math.PR) #Random Matrices and Applications #Secondary 60F10 #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2511.06813

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

We establish large deviation estimates related to the Dynkin--Lamperti theorem, which is a distributional limit theorem for the position of a subordinator immediately before it crosses a fixed level. Our approach relies on the theory of regular variation and the method of the double Laplace transform.

Citations

• Higher order approximations in arcsine laws for subordinators
• Large deviations for occupation and waiting times of infinite ergodic transformations
• Regularity and asymptotics of densities of inverse subordinators
• Local behaviour of the remainder in Renewal theory
• The remainder in the Renewal Theorem
• Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations

Related

• Higher order approximations in arcsine laws for subordinators
• Large deviations for a class of tempered subordinators and their inverse\n processes
• Two non-regular extensions of the large deviation bound
• Two non-regular extensions of large deviation bound
• Large deviations for occupation and waiting times of infinite ergodic transformations