Mathematics Colloquium



Department of Mathematics
University of Nebraska at Omaha


WHEN:
Wednesday March 22, 2:30-3:30PM

WHERE:
Durham Science Center, Room 255

WHAT:


Dr. Steve From

UNO Mathematics


will give a talk on

SOME NEW BOUNDS ON THE EXTINCTION PROBABILITY OF A GALTON-WATSON BRANCHING PROCESS WITH CONNECTIONS TO RELIABILITY THEORY-SOME NUMERICAL COMPARISONS AND CONJECTURES


ABSTRACT:

Various upper and lower bounds exist in the literature concerning the extinction probability of the Galton-Watson branching process. Some simple new lower and upper bounds are derived for this extinction probability. These are numerically compared to many previous bounds discussed in the literature, since analytical comparisons are not usually possible. In addition, we consider some special discrete reliability theory classes, and derive special bounds just for these subclasses. Along the way, some conjectures are suggested. Several examples suggest the validity of these conjectures, yet no proofs have yet been found. (This talk should be accessible to anyone who has had a calculus based prob/stat course and knowledge of power series.)


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