Summary: Current interests
December 8, 2003
The second edition of Applied Probability and Queues was published by
Springer in May 2003.
In 1999 I gave a concentrated advanced course on simulation and wrote
some lecture notes which were posted on the webside of MaPhySto, Aarhus.
Peter Glynn and myself are currently extending and revising these to become
a book. We aim for a general text in simulation covering all important
subareas at a more advanced mathematical level than most other books and
with exercises and examples from a great variety of application areas.
Rare event simulation for heavy tails
This has been a main interest for the last 68 years. A recent contribution
(with Kroese & Rubinstein) is a study of how to use crossentropy (imple
mented via maximum likelihood and subexponential limit theory) for au
tomatic generation of good importance sampling distributions. In work in
progress with Kroese, we have found a new algorithm for random sums (in
particular, the M/G/1 queue and ruin probabilities) which improves substan
tially upon existing ones. It involves conditional Monte Carlo as in earlier