Random walks in $(\mathbb{Z}_+)^2$ with non-zero drift absorbed at the axes

Details Random walks in $(\mathbb{Z}_+)^2$ with non-zero drift absorbed at the axes Random walks in $(\mathbb{Z}_+)^2$ with non-zero drift absorbed at the axes

2009-03-31

arxiv.org/abs/0903.5486v1

Mathematics

Probability

Scientific paper

Spatially homogeneous random walks in $(\mathbb{Z}_{+})^{2}$ with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.

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