Invariance principle for nonhomogeneous random walks on the grid ℤ1

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Abstract

A nonhomogeneous random walk on the grid ℤ1 with transition probabilities that differ from those of a certain homogeneous random walk only at a finite number of points is considered. Trajectories of such a walk are proved to converge to trajectories of a certain generalized diffusion process on the line. This result is a generalization of the well-known invariance principle for the sums of independent random variables and Brownian motion.

Original languageEnglish
Pages (from-to)372-383
Number of pages12
JournalMathematical Notes
Volume66
Issue number3
DOIs
Publication statusPublished - 1999
Externally publishedYes

Keywords

  • Diffusion processes
  • Invariance principle
  • Nonhomogeneous one-dimensional random walk
  • Stochastic semigroups
  • Weak convergence

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