An invariance principle for the local time of a recurrent random walk

1984 ◽  
Vol 66 (1) ◽  
pp. 141-156 ◽  
Author(s):  
Naresh C. Jain ◽  
William E. Pruitt
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Invariance Principle ◽  
Recurrent Random Walk

On the local time of a recurrent random walk on ℤ²

2021 ◽  
Vol 105 (0) ◽  
pp. 69-78
Author(s):  
V. Bohun ◽  
A. Marynych
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Process ◽  
Local Time ◽  
Functional Limit Theorem ◽  
Functional Limit ◽  
Content Type ◽  
Finite Set ◽  
Number Of Visits ◽  
Recurrent Random Walk

We prove a functional limit theorem for the number of visits by a planar random walk on Z 2 \mathbb {Z}^2 with zero mean and finite second moment to the points of a fixed finite set P ⊂ Z 2 P\subset \mathbb {Z}^2 . The proof is based on the analysis of an accompanying random process with immigration at renewal epochs in case when the inter-arrival distribution has a slowly varying tail.

scholarly journals Asymptotic Behavior of the Local Time of a Recurrent Random Walk

1984 ◽  
Vol 12 (1) ◽  
pp. 64-85 ◽  
Author(s):  
Naresh C. Jain ◽  
William E. Pruitt
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Local Time ◽  
Recurrent Random Walk

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

scholarly journals On the local time of random walk on the 2-dimensional comb

2011 ◽  
Vol 121 (6) ◽  
pp. 1290-1314 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Random Walk ◽  
Local Time
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