Speaker: |
Robert Keener |
Title: |
Random Walks Conditioned to Stay Positive |
Abstract: |
Let Sn be a random walk formed by summing i.i.d. integer valued random variables Xi, i ≥ 1: Sn = X1 + · · · + Xn. If the drift EX is negative, then Sn→ −∞ as n → ∞. If An is the event that Sk ≥ 0 for k = 1, . . . , n, then P(An) → 0 as n → ∞. In this talk we will consider conditional distributions for the random walk given An. The main result will show that the finite dimensional distributions given An converge to those for a time homogeneous Markov chain on {0, 1, . . .}.
Download talk (pdf)
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Organizing Committee
Anna Amirdjanova,
Department of Statistics,
University of Michigan Charlie Doering,
Departments of Mathematics and
Physics & MCTP
University of Michigan
Len Sander,
Department of Physics
& MCTP
University of Michigan
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