Minimal subharmonic functions and related integral representations

Umut Cetin

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: one-dimensional diffusions; potential theory; subharmonic functions; integral representation (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2024-01-11
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Published in Electronic Journal of Probability, 11, January, 2024, 29. ISSN: 1083-6489

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