Discrete random walk with geometric absorption

2013/09/04 by Theo van Uem, van Uem, Theo
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G50 #msc:60J10 #primary 60G50 #secondary 60J10

paper · pdf · doi:10.48550/arxiv.1309.0970

4 pages

arxiv created 2013/09/04 · arxiv updated 2013/09/05

Abstract

We consider a discrete random walk (RW) in n dimensions . The RW is adapted with a geometric absorption process: at any discrete time there is a constant probability that absorption occurs in the current state. To model the RW with geometric absorption we use the concept of a multiple function barrier (MFB). In a MFB there is a modification of the original RW: each transition probability in the original RW is multiplied by β and there is an additional probability (1-β) of absorption, where 0<β<1. We study three cases: one-dimensional simple asymmetric RW, n-dimensional simple symmetric RW (n>1) and a two level RW.

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