17th September 2007 — Poisson Processes (@ 12.15)
Change of time: This week the meeting will start at 12:15 instead of the usual time.
We will read J.F.C Kingman's book Poisson Processes. The book is about 100 pages, has nine chapters. We plan to read two chapters each week. We will start with reading Chapters 1 and 2.
Book Description:
In the theory of random processes there are two
that are fundamental, and occur over and over again, often in
surprising ways. There is a real sense in which the deepest results
are concerned with their interplay. One, the Bachelier Wiener model of
Brownian motion, has been the subject of many books. The other, the
Poisson process, seems at first sight humbler and less worthy of study
in its own right. Nearly every book mentions it, but most hurry past
to more general point processes or Markov chains. This comparative
neglect is ill judged, and stems from a lack of perception of the real
importance of the Poisson process. This distortion partly comes about
from a restriction to one dimension, while the theory becomes more
natural in more general context. This book attempts to redress the
balance. It records Kingman's fascination with the beauty and wide
applicability of Poisson processes in one or more dimensions. The
mathematical theory is powerful, and a few key results often produce
surprising consequences.