An inverse problem for the first-passage place of some diffusion processes with random starting point. Issue 6 (1st November 2020)

• Record Type: Journal Article
• Authors: Abundo, Mario
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 6(2020)
• Page Start: 1122
• Page End: 1133
• Publication Date: 2020-11-01
• Subjects: Jump-diffusion process -- first-passage place -- inverse first-passage place problem; 60J60 -- 60H05 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1768867
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We study an inverse problem for the first-passage place of a one-dimensional diffusion process X ( t ) (also with jumps), starting from a random position η ∈ [ a, b ] . Let be τ a, b the first time at which X ( t ) exits the interval ( a, b ), and π a = P ( X ( τ a, b ) ≤ a ) the probability of exit from the left of ( a, b ) . Given a probability q ∈ ( 0, 1 ), the problem consists in finding the density g of η (if it exists) such that π a = q . Some explicit examples are reported.