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Discrete scattering and simple and nonsimple face-homogeneous random walks. (English) Zbl 1140.60320
Summary: We will derive some results for characterizing the almost closed sets of a face-homogeneous random walk. We will present a conjecture on the relation between discrete scattering of the fluid limit and the absence of nonatomic almost closed sets. We will illustrate the conjecture with random walks with both simple and nonsimple decomposition into almost closed sets.
60G50 Sums of independent random variables; random walks
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
Full Text: DOI
[1] DOI: 10.1070/rm1999v054n02ABEH000141 · Zbl 0939.60030 · doi:10.1070/rm1999v054n02ABEH000141
[2] Kaimanovich, Harmonic analysis and discrete potential theory, Frascati, 1991 pp 145– (1992) · doi:10.1007/978-1-4899-2323-3_13
[3] DOI: 10.1017/S0269964803173068 · Zbl 1336.60091 · doi:10.1017/S0269964803173068
[4] DOI: 10.1017/S0269964803173056 · Zbl 1336.60092 · doi:10.1017/S0269964803173056
[5] Hall, Martingale limit theory and its application (1980) · Zbl 0462.60045
[6] Ross, Applied probability models with optimization applications (1970) · Zbl 0213.19101
[7] Fayolle, Constructive theory of countable Markov chains (1995) · Zbl 0823.60053 · doi:10.1017/CBO9780511984020
[8] Williams, Probability with martingales (1991) · Zbl 0722.60001 · doi:10.1017/CBO9780511813658
[9] Chung, Markov chains with stationary transition probabilities (1960) · Zbl 0092.34304 · doi:10.1007/978-3-642-49686-8
[10] Spitzer, Principles of random walk (1976) · Zbl 0359.60003 · doi:10.1007/978-1-4684-6257-9
[11] DOI: 10.1214/aoms/1177728425 · Zbl 0066.11303 · doi:10.1214/aoms/1177728425
[12] DOI: 10.2307/1992904 · Zbl 0071.34901 · doi:10.2307/1992904
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