wjgilbert@watmath.waterloo.edu (William J. Gilbert) (03/08/88)
UNIVERSITY OF WATERLOO
DEPT OF STATISTICS AND ACTUARIAL SCIENCE
AND
FRACTAL GEOMETRY AND DYNAMICAL SYSTEMS SEMINAR SERIES
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TITLE: Self-Similar Processes
SPEAKER: Prof. George O'Brien, Dept of Math, York University
DATE: Thursday, March 10, 1988
TIME: 3:30 p.m.
ROOM: MC 1056
ABSTRACT: A real-valued process X=(X(t)), t in R, is self-similar with
exponent H(H-ss) if X(a.)=sub(d)a^H X for all a>0. Brownian motion is
a major example, as are strictly stable processes. This talk
discusses H-ss processes X_H with stationary increments that can be
represented for t>0 by
X_H(t) = int |x|^H sgn x pi((0,t],dx) = int x pi^H ((0,t],dx)
where pi is a point process in R^2 that is Poincare, i.e. invariant in
distribution under the transformations (t,x) -> (at+b,ax) of R^2.
In particular, X_H allows such a representation if it is a jump
process, pi^H bing the graph of its jumps. Several examples of
Poincare processes pi are presented. These lead in many cases to new
examples of H-ss processes X_H with stationary increments.
Coffee and cake will be served in MC6123 after the talk.
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The next speaker in the Fractal Geometry and Dynamical Systems Seminar
will be
John Holbrook (U. of Guelph) on March 24 (and NOT as advertised)
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