Titlebook: Upper and Lower Bounds for Stochastic Processes; Modern Methods and C Michel Talagrand Book 20141st edition Springer-Verlag Berlin Heidelbe

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书目名称Upper and Lower Bounds for Stochastic Processes被引频次学科排名




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Coterminous

Affable

要求比…更好

Matching Theorems, I,ities occurring in the distribution of . points (..). independently and uniformly distributed in the unit square. These irregularities are measured by the “cost” of pairing (=matching) these points with . fixed points that are very uniformly spread, for two notions of cost. For each of them we prove

明智的人

Cardiac

Trees and the Art of Lower Bounds,tains, in a way which is equivalent to the measures of size introduced in Chapter .. Building a large tree in a metric space is an efficient method to bound its size from below. We apply this idea to prove that the upper bounds obtained in the matching problems of Chapter . are sharp: we prove lower

焦虑

Random Fourier Series and Trigonometric Sums, II, we simply assumed to be independent symmetric r.v.s. This chapter also develops one of the fundamental ideas of this work: many processes can be exactly controlled, not by using one or two distances, but by using an entire family of distances. With these tools, we are able to give in full generalit

Obedient

Processes Related to Gaussian Processes,.-stable processes are conditionally Gaussian to provide lower bounds for such processes. Although these bounds are in general very far from being upper bounds, they are in a sense extremely accurate. In certain situations, where there is “stationarity”, they can be reversed. We obtain these bounds

反复无常

Theory and Practice of Empirical Processes,is direction is whether there exists a “best possible” method to control this supremum at a given size of the random sample. We offer a natural candidate for such a “best possible” method, in the spirit of the Bednorz-Latała result of Chapter 5. Whether this natural method is actually optimal is a m

乐意

Partition Scheme for Families of Distances,refore a whole sequence of distances on the index space. As an application we consider the situation of “canonical processes”, where the r.v.s .. are linear combinations of independent copies of symmetric r.v.s with density proportional to exp(−|.|.) where .≥1 (and to considerably more general situa