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T-Martin boundary of reflected random walks on a half-space
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Irina Ignatiouk-Robert, UMR CNRS 8088, departement de Mathemetiques, Universite de Cergy-Pontoise
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Abstract
The t-Martin boundary of a random walk on a half-space with reflected boundary conditions is identified. It is shown in particular that the t-Martin boundary of such a random walk is not stable in the following sense : for different values of t, the t-Martin compactifications are not equivalent.
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Full text: PDF
Pages: 149-161
Published on: May 19, 2010
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Bibliography
- Billingsley, Patrick. Convergence of
probability measures. John Wiley & Sons, Inc., New
York-London-Sydney 1968 xii+253 pp. MR0233396
(38 #1718)
- Doob, J. L. Discrete potential theory and boundaries.
J. Math. Mech. 8 1959 433--458; erratum
993. MR0107098
(21 #5825)
Dupuis, Paul; Ellis,
Richard S.; Weiss, Alan. Large deviations for Markov processes with
discontinuous statistics. I. General upper bounds. Ann.
Probab. 19 (1991), no. 3, 1280--1297.
MR1112416
(92k:60054)
Dupuis, Paul; Ellis,
Richard S. Large deviations for Markov processes with discontinuous
statistics. II. Random walks. Probab. Theory
Related Fields 91 (1992), no. 2, 153--194.
MR1147614
(93c:60034)
Dupuis, Paul;
Ellis, Richard S. The large deviation principle for
a general class of queueing systems. I. Trans. Amer. Math. Soc.
347 (1995), no. 8, 2689--2751. MR1290716
(96c:60037)
Hunt, G. A. Markoff chains
and Martin boundaries. Illinois J. Math.
4 1960 313--340. MR0123364
(23 #A691)
Ignatiouk-Robert, Irina.
Sample path large deviations and convergence parameters. Ann.
Appl. Probab. 11 (2001), no. 4, 1292--1329.
MR1878299
(2003a:60043)
Ignatiouk-Robert, Irina.
Large deviations for processes with discontinuous statistics. Ann.
Probab. 33 (2005), no. 4, 1479--1508.
MR2150196
(2006m:60029)
Ignatiouk-Robert, Irina.
On the spectrum of Markov semigroups via sample path large
deviations. Probab. Theory Related Fields
134 (2006), no. 1, 44--80. MR2221785
(2007c:60028)
Ignatiouk-Robert, Irina.
Martin boundary of a reflected random walk on a half-space. Probab.
Theory Related Fields (2010), online, DOI:
10.1007/s00440-009-0228-4.
Ignatyuk, I. A.; Malyshev,
V. A.; Shcherbakov, V. V. The influence of boundaries in problems on
large deviations. (Russian) Uspekhi Mat. Nauk
49 (1994), no. 2(296), 43--102; translation
in Russian Math. Surveys 49 (1994), no. 2,
41--99 MR1283135
(96m:60066)
Martin, Robert S. Minimal
positive harmonic functions. Trans. Amer. Math.
Soc. 49, (1941). 137--172. MR0003919
(2,292h)
Molčanov, S. A. Martin
boundary of the direct product of Markov processes. (Russian) Uspehi
Mat. Nauk 22 1967 no. 2 (134) 125--126.
MR0212875
(35 #3740)
Picardello, Massimo A.;
Woess, Wolfgang. Martin boundaries of Cartesian products of Markov
chains. Nagoya Math. J.
128 (1992), 153--169. MR1197035
(94a:60109)
Picardello, Massimo;
Woess, Wolfgang. Examples of stable Martin boundaries of Markov
chains. Potential theory (Nagoya, 1990),
261--270, de Gruyter,
Berlin, 1992. MR1167242
(93f:60115)
Pruitt, William E.
Eigenvalues of non-negative matrices. Ann.
Math. Statist. 35 1964 1797--1800. MR0168579
(29 #5839)
Rockafellar, R. Tyrrell.
Convex analysis. Reprint of the 1970 original. Princeton Landmarks
in Mathematics. Princeton Paperbacks. Princeton
University Press, Princeton, NJ, 1997.
xviii+451 pp. ISBN: 0-691-01586-4 MR1451876
(97m:49001)
Seneta, E. Nonnegative
matrices and Markov chains. Second edition. Springer Series in
Statistics. Springer-Verlag, New York,
1981. xiii+279 pp. ISBN: 0-387-90598-7 MR0719544
(85i:60058)
Woess, Wolfgang. Random
walks on infinite graphs and groups. Cambridge Tracts in
Mathematics, 138. Cambridge University Press,
Cambridge, 2000. xii+334 pp. ISBN:
0-521-55292-3 MR1743100
(2001k:60006)
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