MINI-SEMINAR FOR FIRST-YEAR PH.D. STUDENTS Department of Statistics Rescaling of Marked Point Processesby Zumin Luo Department of Statistics, University of Chicago Wednesday, May 26, 2004, 4:15 pm in Eckhart 110 5734 S. University Avenue |

Fact: Every orthogonal sequence of continuous local martingales can be transformed into a multivariate sequence of independent Brownian motions by rescaling time for each of the martingales via its associated predictable process. Fact: Given a simple multivariate point process, the multivariate point process obtained by rescaling each process according to its compensator is a sequence of independent Poisson processes, each having intensity 1. Question: Can a marked point process be transformed into a compound Poisson process with unit total rate and a fixed mark distribution? |