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Semi-Markov approach to the problem of delayed reflection of diffusion Markov processes


Author: B. P. Harlamov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 13-22
MSC (2010): Primary 60J25, 60J60
DOI: https://doi.org/10.1090/S0094-9000-2015-00931-5
Published electronically: January 26, 2015
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Abstract | References | Similar Articles | Additional Information

Abstract: A one-dimensional diffusion process taking positive values and reflecting from zero is considered. All the variants of reflecting that preserve of the semi-Markov property are described. This property is characterized by a family of Laplace images of times between the first hitting of zero and first hitting of a level $ r$ for any $ r>0$. The parameter of this family is used to construct a time change transforming a process with instantaneous reflection to the process with delayed reflection.


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Additional Information

B. P. Harlamov
Affiliation: Institute of Problems of Mechanical Engineering, RAS, Saint-Petersburg, Russia
Email: b.p.harlamov@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2015-00931-5
Keywords: Diffusion, Markov property, continuous semi-Markov processes, reflection, delaying, first exit time, transition function, Laplace transform, change of time
Received by editor(s): January 30, 2013
Published electronically: January 26, 2015
Additional Notes: This work was supported by grant RFBR 12-01-00457-a
Article copyright: © Copyright 2015 American Mathematical Society