Probability Theory: An Analytic View

By N. H. Bingham. 2002

393 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/afe520df77cfe86f0d13704137758c3c721a12be

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Citations in the corpus

Bellman functions and dimensionless estimates of Littlewood-paley type (2006, background): “In particular, on page 344 of [30] it is written about (4.”
A central limit theorem for convex sets (2006, background): “Corresponding principles also hold for multidimensional marginal distributions of convex sets.”
The Ergodic Theory of Hyperbolic Groups (2011, methodology): “This is a tail event for the sequence of independent random variables zi, so by Kolmogorov’s 0–1 law (see [41] Thm.”
Diffusion limits of the random walk metropolis algorithm in high dimensions (2010, background): “Now, from classical Berry–Esseen estimates (see [26]), we have that”
Smallest singular value of random matrices and geometry of random polytopes (2005, methodology): “The proof of Proposition 3.2 depends on the well-known Berry-Ess¶een theorem (cf., e.g., [ St ]).”
Bulk universality for generalized Wigner matrices (2010, neutral): “30 of [30]).”
Multivariate stochastic bias corrections with optimal transport (2018, background): “For γ ∈ 0(PX,PY), γ (x,y) can be interpreted as the probability that y is the correction of x. Formally, the Jirina theorem (see, e.g., Strook, 1995, chap.”
Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations (2014, background): “Well known textbooks on probability th eory are [4, 14, 15, 44, 45, 37, 71].”
Sub-Gaussian mean estimators (2015, neutral): “Lindberg’s proof of the central limit theorem (see [16]), specialized to the case where X 1 are i.”
Invariance principles for spatial multitype Galton–Watson trees (2006, neutral): “The uniform estimate in Kolmogorov’s criterion [18], Theorem 3.”
Thick points for spatial Brownian motion: multifractal analysis of occupation measure (2000, background): “, [25], page 341), where our condition pθ < q(2)d/2 guarantees that In k ∈ L), and the second inequality comes from the fact that a + b p/2 ≤ a p/2 + b p/2 (since p < 2),”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, background): “Everything up to and including Kolmogorov’s criteria is standard, see [138] or [154] for instance.”