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Asymptotically stable random walks of index $1<\alpha<2$ killed on a finite set. (arXiv:1901.05568v1 [math.PR])
来源于:arXiv
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a
strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic
form of the transition probability for the walk killed when it hits a finite
set. The asymptotic forms obtained are valid uniformly in a natural range of
the space and time variables. The situation is relatively simple when the limit
stable process has jumps in both positive and negative directions; in the other
case when the jumps are one sided rather interesting matters are involved and
detailed analyses are necessitated. 查看全文>>