Andrew Smith

will speak on

Brownian Blancmange and Other Well-Tuned Fractals

Time: 3:00PM
Date: Tue 12th October 2021
Location: Seminar Room SCN 1.25 [map]

Further information

Abstract: The quadratic variation of Fractional Brownian Motion (FBM) on
the unit interval behaves like $n^{1-2H}$ where $n$ (a large
integer) is the number of partitions and $H$ is the Hurst
exponent. This work considers non-stochastic continuous
functions whose quadratic variation behaves like the expected
quadratic variation of FBM for certain sets of integers $n$.
As a special case we investigate Brownian Blancmange, a
generalisation of the Takagi-Landsberg blancmange functions,
whose quadratic variation fits the expected quadratic
variation of Brownian motion when $n$ is either a power of 2,
or 3 times a power of 2. We construct similar examples for
other Hurst exponents. Financial applications include the
construction of stress tests for delta-hedging of investment
guarantees.

This seminar will be face-to-face and online at https://ucd-ie.zoom.us/j/64359336449?pwd=RStYWGpOaDB3U2tsQjQrQWptck1sUT0.

(This talk is part of the Analysis series.)

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