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The asymptotic behavior of a random walk on a dual-medium lattice (1982)

Heyde, C. C. ; Westcott, M. ; Williams, E. R.

Springer

Journal of statistical physics 28 (1982), S. 375-380

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ISSN: 1572-9613

Keywords: Random walk ; anisotropic lattice ; change-point ; diffusion limit ; oscillating Brownian motion

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract This paper considers the asymptotic distribution for the horizontal displacement of a random walk in a medium represented by a two-dimensional lattice, whose transitions are to nearest-neighbor sites, are symmetric in the horizontal and vertical directions, and depend on the column currently occupied. On either side of a change-point in the medium, the transition probabilities are assumed to obey an asymptotic density condition. The displacement, when suitably normalized, converges to a diffusion process of oscillating Brownian motion type. Various special cases are discussed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01012611

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