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Some Results on the Brownian Meander with Drift

Author

Listed:
  • F. Iafrate

    (Sapienza, University of Rome)

  • E. Orsingher

    (Sapienza, University of Rome)

Abstract

In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that $$ \min _{ 0\le z \le t} B(z)> v $$min0≤z≤tB(z)>v with $$ u > v $$u>v. The limiting process for $$ u \downarrow v $$u↓v is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.

Suggested Citation

  • F. Iafrate & E. Orsingher, 2020. "Some Results on the Brownian Meander with Drift," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1034-1060, June.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:2:d:10.1007_s10959-019-00891-3
    DOI: 10.1007/s10959-019-00891-3
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