Bounding the first passage time on an average
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.
Year of publication: |
2004
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Authors: | La Peña, Victor H. De ; Yang, Ming |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 67.2004, 1, p. 1-7
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Publisher: |
Elsevier |
Keywords: | Moment of the first passage time Expectation of a function of the supremum of a nonnegative process |
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