Geodesic
A decomposition for Markov processes at an independent exponential time
Ars Mathematica Contemporanea, Tome 12 (2017) no. 1, pp. 51-65.

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The path of Markov process X run up to an independent exponential random time Sθ can be decomposed into the part prior to the last exit time from a point before Sθ, and the remainder up to Sθ. In this paper the laws of the two segments are identified under suitable assumptions using excursion theory.
DOI : 10.26493/1855-3974.943.2a3
Keywords: Markov proceses, last exit decompositions, excursion theory 
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Mihael Perman. A decomposition for Markov processes at an independent exponential time. Ars Mathematica Contemporanea, Tome 12 (2017) no. 1, pp. 51-65. doi : 10.26493/1855-3974.943.2a3. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.943.2a3/

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