機率研討會

主講者: Professor Fima Klebaner (Monash University)
講題: 1. Martingales with Given Marginals or Fake Brownian Motion, 2. On the Statistical Independence of Primes
時間: 2011-08-11 (Thu.)  15:00 - 17:15
地點: 數學所 722 研討室 (台大院區)
Abstract: 1. We give martingales with N(0,t) marginals which are not a Brownian motion. Such processes have significance in Finance. We also show that there is no such continuous Markov process. Joint work with Kais Hamza, Monash 2. Mark Kac, in his 1959 book "Statistical Independence in Probability, Analysis and Number Theory", states that "the 'events' of being divisible by p and q [2 primes] are independent". This intuitive idea has been extensively used to prove (or reprove) many results in Number Theory. The main approach is to ascribe a "uniform distribution" on the set of integers. This is done via densities and results are of an asymptotic nature. In this talk, we suggest and characterise probability measures on the set of integers under which Kac's statement is made rigorous. We also give related results. Joint work with Kais Hamza, Monash
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