Limit theorems for random walks

Alexander Bendikov, Wojciech Cygan and Bartosz Trojan

Stochastic Processes and their Applications, 2017, vol. 127, issue 10, 3268-3290

Abstract: We consider a random walk Sτ 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 Sτ converges in the Skorohod space to the symmetric α-stable process Bα. We also prove asymptotic formula for the transition function of Sτ similar to the Pólya’s asymptotic formula for Bα.

Keywords: Asymptotic formula; Random walk; Regular variation; Subordination; Strong ratio limit theorem; Functional limit theorem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2017.02.008

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