## Abstract

A nonhomogeneous random walk on the grid ℤ^{1} 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 language | English |
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Pages (from-to) | 372-383 |

Number of pages | 12 |

Journal | Mathematical Notes |

Volume | 66 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 |

Externally published | Yes |

## Keywords

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

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