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Path Collapse for an Inhomogeneous Random Walk

Author

Listed:
  • Ilie Grigorescu

    (University of Miami)

  • Min Kang

    (Northwestern University)

Abstract

On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.

Suggested Citation

  • Ilie Grigorescu & Min Kang, 2003. "Path Collapse for an Inhomogeneous Random Walk," Journal of Theoretical Probability, Springer, vol. 16(1), pages 147-159, January.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:1:d:10.1023_a:1022282505543
    DOI: 10.1023/A:1022282505543
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    References listed on IDEAS

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    1. Ilie Grigorescu & Min Kang, 2002. "Brownian Motion on the Figure Eight," Journal of Theoretical Probability, Springer, vol. 15(3), pages 817-844, July.
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