In English
Föredragshållare: Andrew Barbour
Titel: Poisson--Dirichlet limits for logarithmic combinatorial structures
Sammanfattning: In many classical combinatorial settings, such as assemblies (e.g. permutations), multisets (polynomials over GF(q)) and selections (square free polynomials), the sizes of the largest components of a randomly chosen element have very similar distributions. For instance, Hansen (1994) showed that Shepp and Lloyd's Poisson--Dirichlet limit theorem for random permutations holds for many assemblies and multisets. Here, by exploiting more probabilistic arguments, we can extend her result to all assemblies, multisets and selections in the logarithmic class, as well as to many other structures besides, and we can sharpen it by proving a local limit approximation. (Joint work with R. Arratia and S. Tavaré).
Föredragshållare: Søren Asmussen
Titel: Martingales for Markov-modulated models
Sammanfattning:
For random walks or Lévy processes 
,
the standard Wald martingale is 
where 
. Its extension
to Markov additive processes goes back to work of Keilson &
Wishart in the 60's.
1) We show some new applications of this martingale, in
particular how one can work with some 
for
which the Wald 'martingale' fails to be integrable
or even a local martingale
( 
is then defined in the sense of
analytic continuation).
2) Following work by Kella & Whitt (1992), we suggest a related multidimensional martingale for Markov additive processes with modifications like reflection and give some applications (joint work with Offer Kella, Jerusalem - full text - postscript).
Föredragshållare: Holger Rootzén
Titel: Rates of convergence for extremes
Sammanfattning: This talk discusses some results on the rates of convergence of distributions of maxima and point processes of exceedances for stationary sequences. Further, bounds on the rate of convergence for upcrossings of normal processes in continuous time are developed. The results are obtained by "coupling" and Stein-Chen techniques.
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