On a Markov analogue of continuous-time Q-processes
Author:
Azam A. Imomov
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 84 (2012), 57-64
MSC (2010):
Primary 60J80
DOI:
https://doi.org/10.1090/S0094-9000-2012-00853-3
Published electronically:
July 26, 2012
MathSciNet review:
2857416
Full-text PDF Free Access
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Additional Information
Abstract: The so-called Markov continuous-time $Q$-processes are considered in the paper as a generalization of $Q$-processes. The asymptotic behavior of transition probabilities is studied for Markov $Q$-processes.
References
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- A. A. Imomov, A differential analogue of the main lemma of the theory of Markov branching processes and its application, Ukraïn. Mat. Zh. 57 (2005), no. 2, 258–264 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 57 (2005), no. 2, 307–315. MR 2189330
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References
- K. B. Athreya and P. E. Ney, Branching Processes, Springer, New York, 1972. MR 0373040 (51:9242)
- A. A. Imomov, On a condition of the non-extinction for branching processes, Uzbek Matem. Zhurnal (2001), no. 2, 46–51. (Russian) MR 1943639 (2004c:60239)
- A. A. Imomov, A differential analog of the main lemma of the theory of Markov branching processes and its applications, Ukr. Math. J. 57 (2005), no. 2, 307–315. MR 2189330 (2006i:60120)
- J. Lamperti and P. E. Ney, Conditioned branching processes and their limiting diffusions, Theory Probab. Appl. 13 (1968), 128–139. MR 0228073 (37:3657)
- A. G. Pakes, Some limit theorems for the total progeny of a branching process, Adv. Appl. Probab. 3 (1971), no. 1, 176–192. MR 0283892 (44:1122)
- A. G. Pakes, Some new limit theorems for the critical branching process allowing immigration, Stoch. Process. Appl. 3 (1975), 175–185. MR 0397912 (53:1767)
- A. G. Pakes, On Markov branching processes with immigration, Sankhyā: Indian J. Statist. 37(A) (1975), no. 1, 129–138. MR 0433622 (55:6595)
- B. A. Sevast’yanov, Branching Processes, Nauka, Moscow, 1971; German transl., Verzweigungsprozesse, Akademie-Verlag, Berlin, 1974. MR 0345229 (49:9968)
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Additional Information
Azam A. Imomov
Affiliation:
Department of Probability Theory and Mathematical Statistics, Institute for Mathematics and Information Technologies, Academy of Sciences of Uzbek Republic, Do’rmon Yo’li Street 29, Tashkent 100125, Uzbekistan
Address at time of publication:
Department of Mathematical Analysis and Algebra, Karshi State University, Kuchabag Street 17, Karshi 180103, Uzbekistan
Email:
imomov_azam@mail.ru
Keywords:
Markov $Q$-processes,
transition probability,
stationary measures
Received by editor(s):
November 9, 2009
Published electronically:
July 26, 2012
Dedicated:
Dedicated to the fond memory of Professor I. S. Badalbaev
Article copyright:
© Copyright 2012
American Mathematical Society
