Host Institution: |
La Trobe University |
Title of Seminar: |
Level-crossings of symmetric random walks |
Speaker's Name: |
Prof. Vyacheslav Abramov |
Speaker's Institution: |
School of Mathematical Sciences, Monash University (not current) |
Time and Date: |
Friday 6 May at 2:00 pm (AEST) |
Seminar Abstract: |
Let X(1), X(2), ... be a sequence of independently and identically distributed random variables with EX(1)=0, and let S(0)=0 and S(t)=S(t-1)+X(t), t=1,2,..., be a random walk. Denote tau=inf{t>1: S(t)=0, and 1, otherwise. Let a denote a positive number, and let L(a) denote the number of level-crossings from the below (or above) across the level a during the interval [0,tau]. Under special assumptions, it is proved that there exists an infinitely increasing sequence a(n) such that the equality EL(a(n))=c P{X(1)>0} is satisfied, where c is a specified constant that does not depend on n. The result is illustrated for a number of special random walks. We also give non-trivial examples from queuing theory where the results of this theory are applied. |
Seminar Convenor: |
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AGR IT support: |
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