کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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5130030 | 1378654 | 2017 | 36 صفحه PDF | دانلود رایگان |
We study the transition probability, say pAn(x,y), of a one-dimensional random walk on the integer lattice killed when entering into a non-empty finite set A. The random walk is assumed to be irreducible and have zero mean and a finite variance Ï2. We show that pAn(x,y) behaves like [gA+(x)gÌA+(y)+gAâ(x)gÌAâ(y)](Ï2/2n)pn(yâx) uniformly in the regime characterized by the conditions â£xâ£â¨â£yâ£=O(n) and â£xâ£â§â£yâ£=o(n) generally if xy>0 and under a mild additional assumption about the walk if xy<0. Here pn(yâx) is the transition kernel of the random walk (without killing); gA± are the Green functions for the 'exterior' of A with 'pole at ±â' normalized so that gA±(x)â¼2â£xâ£/Ï2 as xâ±â; and gÌA± are the corresponding Green functions for the time-reversed walk.
Journal: Stochastic Processes and their Applications - Volume 127, Issue 9, September 2017, Pages 2864-2899