Geodesic
Preserving of Markovness whilst delayed reflection
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 157-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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A one-dimensional locally-Markov diffusion process with positive range of values is considered. This process is assumed to be reflected from the point 0. All variants of reflection preserving the semi-Markov property are described. The reflected process prolongs to be locally-Markov in open intervals, but it can loose the global Markov property. The reflection is characterized by $\alpha(r)$ which is the first exit time from semi-interval $[0,r)$ after the first hitting time at 0 (for any $r>0$). A distribution of this time-interval is used for deriving a time change a process with instantaneous reflection into a process with delayed reflection. A process which preserves its markovness after the delayed reflection is proved to have a special distribution of the set of time points when the process has zero meaning during the time $\alpha(r)$. This discontinuum set has exponentially distributed Lebesgue measure. 
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     title = {Preserving of {Markovness} whilst delayed reflection},
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B. P. Harlamov. Preserving of Markovness whilst delayed reflection. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 157-174. http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a9/

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