Probability and random processes (3rd edn)

By David J. Applebaum. 2002

1,094 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

A Kernel Method for the Two-Sample-Problem (2006, background): “propose a third test, which is based on the asymptotic distribution of the unbiased estimate of MMD2 in Lemma 5. Theorem 19 We assume E h2 <∞. Under H 1, MMD2 u converges in distribution (see e.g. Grimmet and Stirzaker, 2001, Section 7.2) to a Gaussian according to m1 2 MMD2 u −MMD 2 [F,p,q] D → ”
On the O(1=k) convergence of asynchronous distributed alternating Direction Method of Multipliers (2013, methodology): “ ˜x = −(D′D)−1D′Hz˜. The next theorem establishes almost sure convergence of the asynchronous ADMM algorithm. Our analysis uses results related to supermartingales (interested readers are referred to [18] and [48] for a comprehensive treatment of the subject). Theorem 4.6: Let {xk,zk,pk} be the sequ”
Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) (2003, background): “from Equation (10) has diagonal elements that are " distributed and off-diagonal elements with expectation zero (Grimmett and Stirzaker 1998).”
Stochastic switching in biology: from genotype to phenotype (2017, neutral): “It can be shown that a persistent state is null if and only if K l 0 nn( ) → as ∞ l → [121].”
Novel scaling limits for critical inhomogeneous random graphs (2009, neutral): “This, in turn, follows when the characteristic function of S ′ t is integrable; see, for example, [21], page 189.”
Kinetics of metal-affinity driven self-assembly between proteins or peptides and CdSe-ZnS quantum dots (2007, neutral): “35,36 For the present solutions, where a ratio of one protein-dye-to-QD was used (low valence), this will imply that in a sample most QDs will bind to one or zero protein, while a smaller fraction will be self-assembled with two or three proteins/peptides.”
Search via quantum walk (2006, background): “in has a unique stationary distribution π= (πx), i.e., a unique left eigenvector πwith eigenvalue 1 and positive coordinates summing up to 1 (for details, see Theorem 1, Section 6.6, page 240 of Ref. [GS01]; Theorem 8.1.22, page 492, and Theorem 8.4.4, page 508, of Ref. [HJ90]). Since we will only c”