An almost sure invariance principle for the range of random walks

DOI10.1016/S0304-4149(98)00053-2zbMath0934.60044MaRDI QIDQ1807273

Yuji Hamana

Publication date: 18 November 1999

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Brownian motionalmost sure invariance principlerange of random walks

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Sample path properties (60G17)

Related Items (11)

Laws of the iterated logarithm for the range of random walks in two and three dimensions ⋮ Range-renewal processes: SLLNs and power laws ⋮ Moderate and small deviations for the ranges of one-dimensional random walks ⋮ On the range of pinned random walks ⋮ Invariance principle for the capacity and the cardinality of the range of stable random walks ⋮ Heat kernel for random walk trace on \(\mathbb Z^{3}\) and \(\mathbb Z^{4}\) ⋮ Exact value of the resistance exponent for four dimensional random walk trace ⋮ On range and local time of many-dimensional submartingales ⋮ Functional CLT for the range of stable random walks ⋮ Some results for range of random walk on graph with spectral dimension two ⋮ An almost sure invariance principle for the range of planar random walks

Cites Work

• Propriétés d'intersection des marches aléatoires. I: Convergence vers le temps local d'intersection. (Properties of intersection of random walks. I: Convergence to local time intersection)
• Further limit theorems for the range of random walk
• The range of transient random walk
• On the number of distinct sites visited by a random walk
• Almost sure invariance principles for partial sums of weakly dependent random variables
• The Law of the Iterated Logarithm for the Range of Random Walk
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