Electronic Communications in Probability

$t$-Martin boundary of reflected random walks on a half-space

Irina Ignatiouk-Robert

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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.

Article information

Electron. Commun. Probab., Volume 15 (2010), paper no. 15, 149-161.

Accepted: 19 May 2010
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 31C35: Martin boundary theory [See also 60J50] 31C05: Harmonic, subharmonic, superharmonic functions 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J50: Boundary theory

t-Martin boundary Markov chain stability

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Ignatiouk-Robert, Irina. $t$-Martin boundary of reflected random walks on a half-space. Electron. Commun. Probab. 15 (2010), paper no. 15, 149--161. doi:10.1214/ECP.v15-1541. https://projecteuclid.org/euclid.ecp/1465243958

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