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Minimal subharmonic functions and related integral representations

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  • Cetin, Umut

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.

Suggested Citation

  • Cetin, Umut, 2024. "Minimal subharmonic functions and related integral representations," LSE Research Online Documents on Economics 121020, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:121020
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    File URL: http://eprints.lse.ac.uk/121020/
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    References listed on IDEAS

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    1. Savas Dayanik, 2008. "Optimal Stopping of Linear Diffusions with Random Discounting," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 645-661, August.
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    More about this item

    Keywords

    one-dimensional diffusions; potential theory; subharmonic functions; integral representation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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