caa a22 4500 605524564 CHVBK 20210128100754.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10958-015-2306-8 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2306-8 Harlamov B. Institute of Problems of Mechanical Engineering of RAS, St. Petersburg, Russia aut Preservation of the Markov Property Under Delayed Reflection [Elektronische Daten] [B. Harlamov] A one-dimensional locally Markov diffusion process with positive range of values is considered. It is assumed that this process is reflected from the point 0. All the variants of reflection with preservation of the semi-Markov property are described. The reflected process is still locally Markov in open intervals, but it can lose the global Markov property. The reflection is characterized by the time α(r) which is the first exit time from the semi-interval [0, r) after the first hitting time at level 0 (for r > 0). A distribution of this time is used to derive a time change transforming a process with instantaneous reflection into a process with delayed reflection. It is proved that a process that preserves its Markov property after the delayed reflection has a special distribution of the set of times at which the process has zero values during the interval [0, α(r)). For such a process, this set has exponentially distributed Lebesgue measure. Bibliography: 7 titles. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/2(2015-04-01), 217-229 1072-3374 206:2<217 2015 206 10958 https://doi.org/10.1007/s10958-015-2306-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2306-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Harlamov B. Institute of Problems of Mechanical Engineering of RAS, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/2(2015-04-01), 217-229 1072-3374 206:2<217 2015 206 10958