Limit theorems for random walks

作者：Bendikov Alexander; Cygan Wojciech; Trojan Bartosz^*

来源：Stochastic Processes and Their Applications, 2017, 127(10): 3268-3290.

DOI：10.1016/j.spa.2017.02.008

• Asymptotic formula
• Random walk
• Regular variation
• Subordination
• Strong ratio limit theorem
• Functional limit theorem

We consider a random walk S-tau 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 tau appropriately scaled random walk S-tau converges in the Skorohod space to the symmetric alpha-stable process B-alpha We also prove asymptotic formula for the transition function of S-tau similar to the Polya's asymptotic formula for B-alpha.

• 出版日期2017-10