On the Asymptotic Behavior of Local Times of Recurrent Random Walks with Finite Variance

1982 ◽  
Vol 26 (4) ◽  
pp. 758-772 ◽  
Author(s):  
A. N. Borodin
Keyword(s):  
Asymptotic Behavior ◽  
Random Walks ◽  
Local Times ◽  
Finite Variance

A note on the asymptotic properties of correlated random walks

1985 ◽  
Vol 22 (4) ◽  
pp. 951-956 ◽  
Author(s):  
J. B. T. M. Roerdink
Keyword(s):  
Asymptotic Behavior ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Simple Relation ◽  
Finite Variance ◽  
Correlated Random Walk ◽  
Expected Number ◽  
Similar Relation ◽  
Correlated Random Walks ◽  
Multistate Random Walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

A note on the asymptotic properties of correlated random walks

1985 ◽  
Vol 22 (04) ◽  
pp. 951-956 ◽  
Author(s):  
J. B. T. M. Roerdink
Keyword(s):  
Asymptotic Behavior ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Simple Relation ◽  
Finite Variance ◽  
Correlated Random Walk ◽  
Expected Number ◽  
Similar Relation ◽  
Correlated Random Walks ◽  
Multistate Random Walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

On the number of times where a simple random walk reaches its maximum

1992 ◽  
Vol 29 (02) ◽  
pp. 305-312 ◽  
Author(s):  
W. Katzenbeisser ◽  
W. Panny
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Probability And Statistics

Let Qn denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important role in probability and statistics. In this paper the distribution and the moments of Qn , are considered and their asymptotic behavior is studied.

Joint asymptotic behavior of local and occupation times of random walk in higher dimension

2007 ◽  
Vol 44 (4) ◽  
pp. 535-563 ◽  
Author(s):  
Endre Csáki ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Unit Ball ◽  
Local Time ◽  
Occupation Time ◽  
Local Times ◽  
Higher Dimension ◽  
Occupation Times ◽  
Symmetric Random Walk

Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

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