Minimal subharmonic functions and related integral representations

Cetin, Umut ORCID: 0000-0001-8905-853X (2024) Minimal subharmonic functions and related integral representations. Electronic Journal of Probability, 29. ISSN 1083-6489

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Abstract

A Choquet-type integral representation result for non-negative subharmonic functions of a one-dimensional regular diffusion is established. The representation allows in particular an integral equation for strictly positive subharmonic functions that is driven by the Revuz measure of the associated continuous additive functional. Moreover, via the aforementioned integral equation, one can construct an Itô-Watanabe pair (g,A) that consist of a subharmonic function g and a continuous additive functional A is with Revuz measure μA such that g(X)exp(−A) is a local martingale. Changes of measures associated with Itô-Watanabe pairs are studied and shown to modify the long term behaviour of the original diffusion process to exhibit transience.

Item Type:	Article
Official URL:	https://projecteuclid.org/journals/electronic-jour...
Additional Information:	© 2024 The Author
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	11 Dec 2023 14:48
Last Modified:	15 Nov 2024 01:48
URI:	http://eprints.lse.ac.uk/id/eprint/121020

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