Limit theorems for random walks

2015/04/07 by Bendikov, Alexander, Cygan, Wojciech, Trojan, Bartosz
#05C81 #44A10 #46F12 #60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1504.01759

Abstract

We consider a random walk S_τ which is obtained from the simple random walk S by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator τ appropriately scaled random walk S_τ converges in the Skorohod space to the symmetric α-stable process B^α. We also prove asymptotic formula for the transition function of S_τ similar to the Pólya's asymptotic formula for B^α.

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