CONDITIONS FOR EXISTENCE AND UNIQUENESS OF THE INVERSE FIRST-PASSAGE TIME PROBLEM APPLICABLE FOR LÉVY PROCESSES AND DIFFUSIONS

• 成果类型: Article
• 署名作者: Klump, Alexander; Savov, Mladen
• 署名单位: Bulgarian Academy of Sciences; University of Sofia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2157
• 发表日期: 2025
• 页码: 1791-1827
• 关键词: free-boundary

摘要

For areal-valued stochastic process (X-t)(t>0) we establish conditions under which the inverse first-passage time problem has a solution for any random variable xi> 0. For Markov processes we give additional conditions under which the solutions are unique and solutions corresponding to ordered initial states fulfill a comparison principle. As examples we show that these conditions include L & eacute;vy processes with infinite activity or unbounded variation and diffusions on an interval with appropriate behavior at the boundaries. Our methods are based on the techniques used in the case of Brownian motion and rely on discrete approximations of solutions via Gamma-convergence from (Theory Probab. Appl. 25 (1980) 362-366) and (Ann. Appl. Probab. 21 (2011) 1663-1693) combined with stochastic ordering arguments adapted from (Theory Probab. Appl. 67 (2023) 570-592).