Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions

Kosuke Yamato

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arXiv · 2408.14163

Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions

Kosuke Yamato

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Abstract

For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through the exit times of the supermartingale, and its existence is shown. We also investigate the absolute continuity relations of the limit laws at time infinity.

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Kosuke Yamato. 2024-08-26. Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions. https://arxiv.org/abs/2408.14163

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