Abstract
A random walk on a two-dimensional lattice with homogeneous rows and inhomogeneous columns, which could serve as a model for the study of some transport phemonema, is discussed. Subject to an asymptotic density condition on the columns it is shown that the horizontal motion of the walk is asymptotically like that of rescaled Brownian motion. Various consequences of this are derived including central limit, iterated logarithm, and mean square displacement results for the horizontal component of the walk.
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References
V. Seshadri, K. Lindenberg, and K. E. Shuler,J. Stat. Phys. 21:517 (1979).
M. Westcott,J. Stat. Phys. 27:75 (1982).
P. Hall and C. C. Heyde,Martingale Limit Theory and its Application (Academic Press, New York, 1980).
S. W. Dharmadhikari, V. Fabian, and K. Jogdeo,Ann. Math. Stat. 39:1719 (1968).
L. Breiman,Probability (Addison-Wesley, Reading, Massachusetts, 1968).
V. Strassen, inProc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 2, p. 315 (1967).
P. Billingsley,Convergence of Probability Measures (Wiley, New York, 1968).
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Heyde, C.C. On the asymptotic behavior of random walks on an anisotropic lattice. J Stat Phys 27, 721–730 (1982). https://doi.org/10.1007/BF01013444
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DOI: https://doi.org/10.1007/BF01013444