2005/05/24 by Víctor M. Hernández Rivero, Victor Rivero, Rivero, Victor
Business, Management and Accounting · Decision Sciences · Mathematics · #FOS: Mathematics #MSC: 60G30 (60G51) #Probability (math.PR) #Probability and Risk Models #Supply Chain and Inventory Management #math.PR #msc:60G30
paper · pdf · doi:10.48550/arxiv.math/0505495
26 pages, 24 Mai 2005
arxiv created 2005/05/24 · openalex publication_date 2005/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the upward ladder height subordinator H associated to a real valued Lévy process ξ has Laplace exponent ϕ that varies regularly at ∞ (resp. at 0) if and only if the underlying Lévy process ξ satisfies Sinai's condition at 0 (resp. at ∞). Sinai's condition for real valued Lévy processes is the continuous time analogue of Sinai's condition for random walks. We provide several criteria in terms of the characteristics of ξ to determine whether or not it satisfies Sinai's condition. Some of these criteria are deduced from tail estimates of the Lévy measure of H, here obtained, and which are analogous to the estimates of the tail distribution of the ladder height random variable of a random walk which are due to Veraverbeke and Grübel