Abstract
Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces.
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Hörmander L (1990) An introduction to complex analysis in several variables. North-Holland Mathematical Library, vol 7, 3rd edn. North-Holland, Amsterdam, p xii+254. (3rd edition of An introduction to complex analysis in several variables, D. Van Nostrand, Princeton, 1966, x+208 pp)
Markushevich AI (1985) Theory of functions of a complex variable. Vol I, II, III, 2nd edn. Chelsea, New York, p xxiii+1138. (English edition: Theory of analytic functions. GITTL, Moscow, 1950)
Silvestrov D, Silvestrov S (2017) Asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes. 1. Method Comp Appl Probab. https://doi.org/10.1007/s11009-017-9605-0
Silvestrov D, Silvestrov S (2016a) Asymptotic expansions for stationary distributions of perturbed semi-Markov processes. In: Silvestrov S, Ranc̆ić M (eds) Engineering mathematics II. Algebraic, stochastic and analysis structures for networks, data classification and optimization. Chapter 10. Springer proceedings in mathematics & statistics, vol 179. Springer, Cham, pp 151–222
Silvestrov D, Silvestrov S (2016b) Asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes. I, II. Part I: arXiv:1603.04734, 30 pp. Part II: arXiv:1603.04743, 33 pp
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Silvestrov, D., Silvestrov, S. Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2. Methodol Comput Appl Probab 21, 965–984 (2019). https://doi.org/10.1007/s11009-017-9607-y
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DOI: https://doi.org/10.1007/s11009-017-9607-y
Keywords
- Markov chain
- Semi-Markov process
- Nonlinear perturbation
- Stationary distribution
- Expected hitting time
- Laurent asymptotic expansion