作者：Yao, Yi-Ching
作者单位：Academia Sinica - Taiwan; Colorado State University System; Colorado State University Fort Collins
摘要：For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov's theorem states that the k-record processes, k = 1, 2,..., are i.i.d. A new proof is given which is based on a continualization'' argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particul...
作者：Assaf, David
作者单位：Hebrew University of Jerusalem
摘要：A continuous time Markov chain is observed with Gaussian white noise added to it. To the well-known problem of continuously estimating the current state of the chain, we introduce the additional option of continuously varying the sampling rates, as long as some restriction (or cost) on the average sampling rate is satisfied. The optimal solution to this dynamic sampling problem is presented and analyzed in closed form for the two-state symmetric case. It is shown that the resulting dynamic sam...
