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| Content Provider | Springer Nature Link |
|---|---|
| Author | Appelt, Mirjam Heinrich, Lothar |
| Copyright Year | 2014 |
| Abstract | We consider the random walk of a particle on the two-dimensional integer lattice starting at the origin and moving from each site (independently of the previous moves) with equal probabilities to any of the four nearest neighbors. When τ $_{ i }$ denotes the even number of steps between the (i − 1)th and ith returns to the origin, we shall prove that the geometric mean of τ $_{1}$ , . . . , τ $_{ n }$ divided by n $^{ π }$ converges in distribution to some positive random variable having a logarithmic stable law. We also obtain a rate of this convergence and improve the asymptotic estimate of the tail probability of τ $_{1}$ obtained by Erdos and Taylor (1960). |
| Ending Page | 322 |
| Page Count | 15 |
| Starting Page | 308 |
| File Format | |
| ISSN | 03631672 |
| e-ISSN | 15738825 |
| Journal | Lithuanian Mathematical Journal |
| Issue Number | 3 |
| Volume Number | 54 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2014-08-02 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | simple random walk elliptic integral of first kind Esseen’s inequality Characteristic functions; other transforms Probability Theory and Stochastic Processes Mathematics Actuarial Sciences geometric mean Euler–Mascheroni constant first return time Ordinary Differential Equations Elliptic integrals as hypergeometric functions square lattice Number Theory Central limit and other weak theorems characteristic function Sums of independent random variables; random walks asymptotic expansion |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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