Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales | Zendy

Mikhail Urusov | Zendy; Mihail Zervos | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales

Author(s) -

Mikhail Urusov,

Mihail Zervos

Publication year - 2017

Publication title -

electronic communications in probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.236

H-Index - 38

ISSN - 1083-589X

DOI - 10.1214/17-ecp42

Subject(s) - mathematics , martingale (probability theory) , wedge (geometry) , local martingale , combinatorics , geometry , statistics

We consider the decreasing and the increasing r-excessive functions φr and ψr that are associated with a one-dimensional conservative regular continuous strong Markov process X with values in an interval with endpoints α < β. We prove that the rexcessive local martingale ( eφr(Xt∧Tα) ) ( resp., ( e−r(t∧Tβ ψr(Xt∧Tβ ) )) is a strict local martingale if the boundary point α (resp., β) is inaccessible and entrance, and a martingale otherwise. AMS 2010 Subject Classification: 60G44, 60G48, 60J60

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research