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Financial/Actuarial Mathematics Seminar

The Coin-turning Walk and Its Scaling Limit
Wednesday, December 9, 2020
4:00-5:00 PM
https://umich.zoom.us/j/95407665241 Off Campus Location
Let S be the random walk obtained from “coin turning" with some sequence {p_n}n≥2, where {p_n}n≥2 is a given sequence of the probabilities to "turn the coin" at step n. In this paper we investigate the scaling limits of S in the spirit of the classical Donsker invariance, both for the heating and for the cooling dynamics.
We prove invariance principles, albeit with a non-classical scaling, holds for “not too small" sequences. The order const·n−1 (critical cooling regime) being the threshold. At and below this critical order, the scaling behavior is dramatically different from the one above it. The same order is also the critical one for the Weak Law of Large Numbers to hold.
In the critical cooling regime, an interesting process emerges: it is a continuous, piecewise linear, recurrent process, for which the one-dimensional marginals are Beta-distributed. Speaker(s): Zhenhua Wang (UM)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics