**ELEC 697: Introduction to Multifractals
(1997)**
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Time/Location

Tuesday, Thursday: 8:50- 10:15 am, Duncan Hall 2014
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My office

Duncan Hall 2025, x 3020. Please, schedule meetings by email.
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Syllabus

Cascades are random processes which are constructed appying a *multiplicative*
iteration scheme. Since they are multiscale in nature, they are best fit
to model *positive* long-range-dependent (LRD) data, such as traffic
loads. However, being multiplicative cascades possess a multi-fractal structure
which describe their dependence structure which is more complex than the
second-order LRD.
In this course we start with an introduction to the mathematical background
of fractals, iteration and dimensions. With deterministic cascades
we then explain the principles of multifractal analysis, in particular
its relation to Large Deviations: the multifractal spectrum compactly represents
the frequency of rare events, such as bursts in traffic loads, and goes,
thus, beyond a global (almost sure) description. We round up the
course by a chapter on random cascades.

Homework will be assigned on an irregular basis. Students who wish to
claim credit are expected to do a project which may consist of presenting
a research article or programming. Only a basic course in probability (ELEC
533) is required.