Probability and Random Processes

By Stergios B. Fotopoulos. Technometrics, 2007

572 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1c55a1d302a98dbd778be21dd0d9c2c8acfa44f9

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Citations in the corpus

Bayesian reasoning and machine learning (2012, unknown): “18) In other words, p is the eigenvector of M with eigenvalue 1[122].”
Unsupervised Large-Vocabulary Word Sense Disambiguation with Graph-based Algorithms for Sequence Data Labeling (2005, unknown): “Based on the Ergodic theorem for Markov chains (Grimmett and Stirzaker, 1989), the algorithm is guaranteed to converge if the graph is both aperiodic and irreducible.”
Application of the complex multivariate normal distribution to crystallographic methods with insights into multiple isomorphous replacement phasing. (2003, unknown): “This relationship is a property of independent variables, for which the product of expected values is equal to the expected value of a product (e.g. Grimmett & Stirzaker, 1992).”
Decentralized RLS With Data-Adaptive Censoring for Regressions Over Large-Scale Networks (2016, unknown): “Proof: We need the following lemma in [8, Chapter 7, Theorem 4].”
TensorCast: forecasting and mining with coupled tensors (2018, background): “…b follow power-laws with exponents α a and α b , then a randomly drawn element from any rank-1 frontal slice created as Proof Let X and Y follow power-law distributions of the form Then Z = XY has probability distribution [13], p. 109): which tends to a power-law with exponent − min (α a , α b ) .”
Stochastic geometry and random graphs for the analysis and design of wireless networks (2009, methodology): “Note that since the existence of an in ﬁ nite cluster does not depend on the state of a ﬁ nite number of edges, we can use Kolmogorov’s zero-one law to conclude that the probability that such a cluster exists is either zero or one (see e.g. , [64]).”
Marginal multi-bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member (2012, background): “…measurement likelihood, and the set integral is defined as: [5, p361] g(X)δX g(∅) + ∞ n=1 1 n! g({x 1 , . . . , x n })dx 1 · · · dx n (4) Probability generating functions (pgfs) are widely used in queueing systems, etc, as they greatly simplify analysis of independent random variables (e.g., [20]).”