Titlebook: Upper and Lower Bounds for Stochastic Processes; Decomposition Theore Michel Talagrand Book 2021Latest edition Springer Nature Switzerland

嘲笑

Unfulfilled DreamsWe state a number of daring conjectures concerning the boundedness of random series of functions with non-negative summands are the special setting of selector processes.

执

Empirical Processes, IIWe provide a sample of the deep methods used to bound empirical processes by proving two recent results.

厌恶

Gaussian ChaosWe study order 2 Gaussian chaos and the tails of higher-order chaos.

分解

Convergence of Orthogonal Series: Majorizing MeasuresWe study order 2 Gaussian chaos and the tails of higher-order chaos.

Militia

Michel TalagrandPresents complete proofs of deep results in probability.Provides essential tools and methods.Discusses a number of classical problems and fundamental open questions

reperfusion

Random Fourier Series and Trigonometric Sumst conditions take the form of a smallness condition of the underlying compact group for such a family of distances. We prove our first decomposition theorems. In words, one of these theorems states that if a random Fourier series converges a.s., it can be decomposed in the sum of three random Fourier series, each of which converges a.s.

POINT

Bernoulli Processess already bounded. Second, it may happen that the sum of the absolute values of the coefficients of the random signs is already bounded. We state the Bernoulli conjecture, which asserts that every situation is a combination of these.

comely

flourish

Gaussian Processes and the Generic Chainingistance which suitably controls the increments of the process. We describe the generic chaining and the construction of suitable sequences of partitions in metric spaces, the characterization of sample boundedness of Gaussian processes, and the size of ellipsoids in Hilbert spaces.

丰满有漂亮