Central limit theorem for a class of nonhomogeneous random walks

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Abstract

A spatially nonhomogeneous random walk η t on the grid ℤ v = ℤ m x ℤ n is considered. Let η t 0 be a random walk homogeneous in time and space, and let η t be obtained from it by changing transition probabilities on the set A = Ā x ℤ n, \Ā\ < ∞ so that the walk remains homogeneous only with respect to the subgroup ℤ n of the group ℤ v. It is shown that if m ≥ 2 or the drift is distinct from zero, then the central limit theorem holds for η t.

Original languageEnglish
Pages (from-to)690-695
Number of pages6
JournalMathematical Notes
Volume69
Issue number5-6
Publication statusPublished - May 2001
Externally publishedYes

Keywords

  • Central limit theorem
  • Markov process
  • Random walk on the grid
  • Stochastic operators
  • Weak convergence

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