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α-stable random walk has massive thorns

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Bendikov A., Cygan W.

Colloquium Mathematicum

2015

tom 138

nr 1

105-129

We introduce and study a class of random walks defined on the integer lattice $ℤ^{d}$-a discrete space and time counterpart of the symmetric α-stable process in $ℝ^{d}$. When 0 < α <2 any coordinate axis in $ℤ^{d}$, d ≥ 3, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.

Long time behavior of random walks on abelian groups

100%

Bendikov A., Bobikau B.

Colloquium Mathematicum

2010

tom 118

nr 2

445-464

Let 𝔾 be a locally compact non-compact metric group. Assuming that 𝔾 is abelian we construct symmetric aperiodic random walks on 𝔾 with probabilities $n ↦ ℙ(S_{2n} ∈ V)$ of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups 𝔾, the decay of the function $n ↦ ℙ(S_{2n} ∈ V)$ can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on 𝔾.

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2 Colloquium Mathematicum

2 Bendikov A.

1 Bobikau B.

1 Cygan W.

1 2015

1 2010

Wyniki wyszukiwania

α-stable random walk has massive thorns

Long time behavior of random walks on abelian groups