We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1 topology and fails to hold in the J1 topology.
Avram, F. and Taqqu, M. S., Weak convergence of sums of moving averages in the α-stable domain of attraction, The Annals of Probability, 201483–503 (1992).
Avram, F. and Taqqu, M. S., Weak convergence of sums of moving averages in the α-stable domain of attraction, The Annals of Probability, 201483–503 (1992).)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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