Geodesic
Optimal local first exit time
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 83-108 
S. S. Rasova; B. P. Harlamov. Optimal local first exit time. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 83-108. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a6/
@article{ZNSL_2008_361_a6,
     author = {S. S. Rasova and B. P. Harlamov},
     title = {Optimal local first exit time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {83--108},
     year = {2008},
     volume = {361},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A random process and the corresponding class of so called local first exit times are considered. For a special functional depending on Markov times the problem to find the optimal one is investigated. A description of the class is obtained. For diffusion Markov processes the folowing alternative is proved: either the global first exit time is optimal (trivial case), or in the given class there are no optimal Markov times. For a non-Markov piece-wise increasing process a non-trivial example of the local first exit time is constructed. An application of the problem to insurance is discussed. Bibl. – 7 titles.

[1] V. F. Zaitsev, A. D. Polyanin, Spravochnik po obyknovennym differentsialnym uravneniyam, Fizmatlit, M., 2001 | MR | Zbl

[2] S. S. Rasova, “Vybor momenta nachala strakhovaniya pri nemonotonnoi degradatsii”, Vestnik SPbGU. Ser. 1, 2007, no. 4, 83–95

[3] B. P. Kharlamov, “Optimalnyi rezhim obsluzhivaniya sistemy s nablyudaemoi opasnostyu otkazov”, Avtomatika i telemekhanika, 1998, no. 4, 117–134 | MR | Zbl

[4] B. P. Kharlamov, Nepreryvnye polumarkovskie protsessy, Nauka, SPb., 2001 | MR | Zbl

[5] B. P. Kharlamov, “O vybore momenta nachala strakhovaniya”, Avtomatika i telemekhanika, 2003, no. 7, 134–142 | MR | Zbl

[6] B. P. Kharlamov, “Obraschennyi protsess s nezavisimymi polozhitelnymi prirascheniyami: konechnomernye raspredeleniya”, Zap. nauchn. semin. POMI, 311, POMI, SPb., 2004, 286–297 | MR | Zbl

[7] B. P. Harlamov, “Optimal prophylaxis policy for systems with partly observable parameters”, Statistical and Probabilistic Models in Reliability, eds. V. Ionescu, N. Limnios, Birkhäuser, Boston, 1999, 265–278 | MR