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Some conditional crossing results of Brownian motion over a piecewise-linear boundary


  • Abundo, Mario


Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,T], a piecewise-linear function S(t), with the condition that the value of Bt is assigned at a future time u>T or at an intermediate time u

Suggested Citation

  • Abundo, Mario, 2002. "Some conditional crossing results of Brownian motion over a piecewise-linear boundary," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 131-145, June.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:131-145

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    References listed on IDEAS

    1. De Dominicis, Rodolfo, 1983. "Asymptotic normal distribution of multidimensional statistics of dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 302-309, June.
    2. Ellis, Richard S. & Wang, Kongming, 1990. "Limit theorems for the empirical vector of the Curie-Weiss-Potts model," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 59-79, June.
    3. Wang, Kongming, 1994. "Solutions of the variational problem in the Curie--Weiss--Potts model," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 245-252, April.
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    Cited by:

    1. Abundo, Mario, 2012. "An inverse first-passage problem for one-dimensional diffusions with random starting point," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 7-14.
    2. Abundo, Mario, 2013. "The double-barrier inverse first-passage problem for Wiener process with random starting point," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 168-176.
    3. Klepper, Steven & Thompson, Peter, 2010. "Disagreements and intra-industry spinoffs," International Journal of Industrial Organization, Elsevier, vol. 28(5), pages 526-538, September.
    4. Bischoff, Wolfgang & Hashorva, Enkelejd, 2005. "A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 265-271, October.
    5. Atkinson, Michael P. & Singham, Dashi I., 2015. "Multidimensional hitting time results for Brownian bridges with moving hyperplanar boundaries," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 85-92.


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