Mathematical Sciences: Exchangeability

研究人员将继续他在可互换性方面的研究。这位研究人员是最近可交换性活动的发起人之一，并且已经在这方面做了大量的工作。可交换性是一类概率分布的性质，它刻画了变换下的某些不变性。对于变量序列，可交换性是一个非常弱的假设性质，因此，了解有多少“经典”结果扩展到这种相依的随机变量序列是非常重要的。研究者已经证明了一些与过滤、停时和随机积分有关的结果。他将继续在这些领域进行研究。

The investigator will continue his research in exchangeability. The investigator is one of the originators of the recent activity in exchangeability and has done extensive work in it already. Exchangeability is a property of classes of probability distributions that characterizes certain invariance properties under transformations. Exchangeability is a very weak property to assume for a sequence of variables and hence it is very important to see how many "classical"results extend to such dependent sequences of random variables. The investigator has already proved a number of results related to filtration, stopping times and stochastic integrals. He will continue his research in these areas.