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Limit laws for Brownian motion conditioned to reach a high level

Author

Listed:
  • Klass, Michael
  • Pitman, Jim

Abstract

A functional limit theorem is presented for the behaviour of Brownian motion conditioned to reach a high level during a fixed time interval. The asymptotic behaviour of the conditioned path as the level tends to infinity is related to Williams' path decomposition at the maximum.

Suggested Citation

  • Klass, Michael & Pitman, Jim, 1993. "Limit laws for Brownian motion conditioned to reach a high level," Statistics & Probability Letters, Elsevier, vol. 17(1), pages 13-17, May.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:1:p:13-17
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