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Bounding the first passage time on an average

Author

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  • De La Peña, Victor H.
  • Yang, Ming

Abstract

Let [zeta]t, t[greater-or-equal, slanted]0, be a process taking nonnegative values, Tr=inf{t>0;[zeta]t>r}, r>0, and [psi] a nondecreasing function. An interesting question is: Is it possible to bound E[psi](Tr) above and below by expectations of functions of [zeta]t? We answer this question and give the desired upper and lower bounds.

Suggested Citation

  • De La Peña, Victor H. & Yang, Ming, 2004. "Bounding the first passage time on an average," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 1-7, March.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:1:p:1-7
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    Cited by:

    1. Michael J. Klass & Ming Yang, 2012. "Maximal Inequalities for Additive Processes," Journal of Theoretical Probability, Springer, vol. 25(4), pages 981-1012, December.
    2. Brown, Mark & de la Peña, Victor H. & Klass, Michael J. & Sit, Tony, 2016. "On an approach to boundary crossing by stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3843-3853.

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