Exact and asymptotic properties of multistate random walks

1991 ◽  
Vol 65 (1-2) ◽  
pp. 167-182 ◽  
Author(s):  
Carlos B. Briozzo ◽  
Carlos E. Budde ◽  
Omar Osenda ◽  
Manuel O. C�ceres
Keyword(s):  
Random Walks ◽  
Asymptotic Properties ◽  
Multistate Random Walks

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.

Asymptotic properties of multistate random walks. I. Theory

1985 ◽  
Vol 40 (1-2) ◽  
pp. 205-240 ◽  
Author(s):  
J. B. T. M. Roerdink ◽  
K. E. Shuler
Keyword(s):  
Random Walks ◽  
Asymptotic Properties ◽  
Multistate Random Walks

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.

scholarly journals On the csáki-vincze transformation

2013 ◽  
Vol 50 (2) ◽  
pp. 266-279
Author(s):  
Hatem Hajri
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Scaling Limit ◽  
Simple Random Walk ◽  
Precise Description ◽  
Discrete Transformation

Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T. We prove that T is exact: ∩k≧1σ(Tk(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T “converge” to the corresponding iterations of the continuous Lévy transform of Brownian motion.

ASYMPTOTIC PROPERTIES OF RANDOM WALKS ON p-ADIC SPACES

1991 ◽  
Vol 06 (13) ◽  
pp. 1199-1201 ◽  
Author(s):  
J.L. LUCIO ◽  
Y. MEURICE
Keyword(s):  
Scalar Field ◽  
Lower Bound ◽  
Random Walks ◽  
Average Distance ◽  
Asymptotic Properties ◽  
Field Theories ◽  
Critical Dimensions

We give an upper and a lower bound for the average distance covered after n steps for a family of random walks on a D-dimensional p-adic space. We mention the implications of this result for the critical dimensions of scalar field theories on such a space.

Comportement asymptotique des marches aleatoires associees aux polynomes de Gegenbauer et applications

1984 ◽  
Vol 16 (2) ◽  
pp. 293-323 ◽  
Author(s):  
Leonard Gallardo
Keyword(s):  
Fourier Transform ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Random Walks ◽  
Orthogonal Polynomials ◽  
Comparison Theorem ◽  
Asymptotic Properties ◽  
Basic Tool ◽  
Independent Increments ◽  
Gegenbauer’S Polynomials

Random walks on N associated with orthogonal polynomials have properties similar to classical random walks on . In fact such processes have independent increments with respect to a hypergroup structure on with a convolution and a Fourier transform which is the basic tool for their study. We illustrate these ideas by giving a description of the asymptotic behaviour (CLT and ILL) of the random walks associated with Gegenbauer's polynomials. Moreover we can then use these random walks as a reference scale to deduce asymptotic properties of other Markov chains on via a comparison theorem which is of independent interest.

scholarly journals A general discrete-time modeling framework for animal movement using multistate random walks

2012 ◽  
Vol 82 (3) ◽  
pp. 335-349 ◽  
Author(s):  
Brett T. McClintock ◽  
Ruth King ◽  
Len Thomas ◽  
Jason Matthiopoulos ◽  
Bernie J. McConnell ◽  
...  
Keyword(s):  
Random Walks ◽  
Discrete Time ◽  
Animal Movement ◽  
Modeling Framework ◽  
Time Modeling ◽  
Multistate Random Walks ◽  
Discrete Time Modeling

Random walks on finite semigroups

1998 ◽  
Vol 35 (04) ◽  
pp. 824-832
Author(s):  
George R. Barnes ◽  
Patricia B. Cerrito ◽  
Inessa Levi
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Algebraic Structure ◽  
Asymptotic Properties ◽  
Transition Matrices ◽  
Finite Semigroups ◽  
Block Diagonal

The purpose of this paper is to study the asymptotic properties of Markov chains on semigroups. In particular, the structure of transition matrices representing random walks on finite semigroups is examined. It is shown that the transition matrices associated with certain semigroups are block diagonal with identical blocks. The form of the blocks is determined via the algebraic structure of the semigroup.

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