A stable limit law for recurrence times of the simple random walk on the two-dimensional integer lattice

DOI10.1007/s10986-014-9245-9zbMath1297.60027OpenAlexW2034845809MaRDI QIDQ406619

Mirjam Appelt, Lothar Heinrich

Publication date: 8 September 2014

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-014-9245-9

zbMATH Keywords

asymptotic expansioncharacteristic functiongeometric meansimple random walksquare latticeEsseen's inequalityEuler-Mascheroni constantfirst return timeelliptic integral of first kind

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Sums of independent random variables; random walks (60G50) Elliptic integrals as hypergeometric functions (33C75)

Cites Work

• An asymptotic expansion in the case of a stable approximation law
• Some problems concerning the structure of random walk paths
• LIMIT DISTRIBUTIONS OF SOME STEREOLOGICAL ESTIMATORS IN WICKSELL'S CORPUSCLE PROBLEM
• Rates of Convergence in Stable Limit Theorems for Sums of Exponentially Ψ-mixing Random Variables with an Application to Metric Theory of Continued Fractions
• Numerical calculation of stable densities and distribution functions
• Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
• Random Walk in Random and Non-Random Environments
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