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The first exit time of fractional Brownian motion from the minimum and maximum parabolic domains

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  • Lu, Dawei
  • Zhou, Yinbing

Abstract

Consider a fractional Brownian motion starting at an interior point of the minimum and maximum parabolic domains, namely, Dmin=x,y1,y2:‖x‖0, and p1,p2>1. Let τmin and τmax denote the first times that the fractional Brownian motion exits from Dmin and Dmax, respectively. Asymptotically equivalent estimates of logPτmin>t and logPτmax>t are respectively given by using Gordon’s inequality, depending on the relationship between p1 and p2. The proof methods are based on early works of Li, Shi, Lifshits, Aurzada and Lu.

Suggested Citation

  • Lu, Dawei & Zhou, Yinbing, 2022. "The first exit time of fractional Brownian motion from the minimum and maximum parabolic domains," Statistics & Probability Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000578
    DOI: 10.1016/j.spl.2022.109467
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    References listed on IDEAS

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    1. Dawei Lu & Lixin Song, 2011. "The First Exit Time of a Brownian Motion from the Minimum and Maximum Parabolic Domains," Journal of Theoretical Probability, Springer, vol. 24(4), pages 1028-1043, December.
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