The Annals of Applied Probability

Positive recurrence of processes associated to crystal growth models

E. D. Andjel, M. V. Menshikov, and V. V. Sisko

Full-text: Open access

Abstract

We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather natural condition.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 3 (2006), 1059-1085.

Dates
First available in Project Euclid: 2 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1159804975

Digital Object Identifier
doi:10.1214/105051606000000079

Mathematical Reviews number (MathSciNet)
MR2260057

Zentralblatt MATH identifier
1107.60071

Subjects
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 60G55: Point processes 60K25: Queueing theory [See also 68M20, 90B22] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 80A30: Chemical kinetics [See also 76V05, 92C45, 92E20]

Keywords
Positive recurrent Markov chain invariant measure exponentially decaying tails

Citation

Andjel, E. D.; Menshikov, M. V.; Sisko, V. V. Positive recurrence of processes associated to crystal growth models. Ann. Appl. Probab. 16 (2006), no. 3, 1059--1085. doi:10.1214/105051606000000079. https://projecteuclid.org/euclid.aoap/1159804975


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References

  • Brémaud, P. (1981). Point Processes and Queues. Springer, New York.
  • Fayolle, G., Malyshev, V. A. and Menshikov, M. V. (1995). Topics in Constructive Theory of Countable Markov Chains. Cambridge Univ. Press.
  • Gates, D. J. and Westcott, M. (1988). Kinetics of polymer crystallization I. Discete and continuum models. Proc. Roy. London Soc. Ser. A 416 443–461.
  • Gates, D. J. and Westcott, M. (1993). Markov models of steady crystal growth. Ann. Appl. Probab. 3 339–355.