Conditioning subordinators embedded in Markov processes

Andreas E. Kyprianou; Victor Rivero; Bati Sengul

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arXiv · 1506.07870

Conditioning subordinators embedded in Markov processes

Andreas E. Kyprianou·Victor Rivero·Bati Sengul

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Abstract

The running infimum of a Levy process relative to its point of issue is know to have the same range that of the negative of a certain subordinator. Conditioning a Levy process issued from a strictly positive value to stay positive may therefore be seen as implicitly conditioning its descending ladder heigh subordinator to remain in a strip. Motivated by this observation, we consider the general problem of conditioning a subordinator to remain in a strip. Thereafter we consider more general contexts in which subordinators embedded in the path decompositions of Markov processes are conditioned to remain in a strip.

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Andreas E. Kyprianou, Victor Rivero, Bati Sengul. 2015-06-25. Conditioning subordinators embedded in Markov processes. https://arxiv.org/abs/1506.07870

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