Abstract
We examine the convexity of the hitting distribution of the real axis for symmetric random walks on ℤ2. We prove that for a random walk starting at (0, h), the hitting distribution is convex on [h − 2, ∞) ∩ ℤ if h ≥ 2. We also show an analogous fact for higher-dimensional discrete random walks. This paper extends the results of a recent paper [NT].
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Acknowledgements
This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4.A/2-11-1-2012-0001 ‘National Excellence Program’.
Supported by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A-11/1/KONV-2012-0073”.
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Nagy, G.V., Szalai, A. On the convexity of a hitting distribution for discrete random walks. ActaSci.Math. 82, 305–312 (2016). https://doi.org/10.14232/actasm-014-526-1
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DOI: https://doi.org/10.14232/actasm-014-526-1