A minisymposium is arranged on December 4th 1997 with lectures by
Søren Asmussen,
Andrew Barbour
och
Holger Rootzén
Speaker: Andrew Barbour
Title: Poisson--Dirichlet limits for logarithmic combinatorial structures
Abstract: 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).
Speaker: Søren Asmussen
Title: Martingales for Markov-modulated models
Abstract: 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).
Speaker: Holger Rootzén
Title: Rates of convergence for extremes
Abstract: 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.
Senast modifierad - last change 1997-11-10
Webansvarig: Gunnar Englund - gunnare@math.kth.se