Invariance principle for nonhomogeneous random walks on the grid ℤ1

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number3
Publication statusPublished - 1999
Externally publishedYes


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


Dive into the research topics of 'Invariance principle for nonhomogeneous random walks on the grid ℤ1'. Together they form a unique fingerprint.

Cite this