Level-crossings of symmetric random walks

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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