An almost sure invariance principle for the range of random walks

Yuji Hamana

Stochastic Processes and their Applications, 1998, vol. 78, issue 2, 131-143

Abstract: The range of random walks means the number of distinct sites visited at least once by the random walk before time n. We study an almost sure invariance principle for the range of random walks on the four or more dimensional integer lattice and obtain that the centralized and linearly interpolated range of the random walk can be asymptotically equal to a Brownian motion almost surely.

Keywords: Almost; sure; invariance; principle; Range; of; random; walks; Skorohod's; representation; theorem (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (5)

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