Foundations of modern probability

By G. Leversha. Mathematical Gazette, 2004

466 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/786d230692dd7a0a03202395bb41f1333e51b86e

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Citations in the corpus

Asymptotics for sliced average variance estimation (2007, unknown): “11 of [15], we have E(A22n) = o(cn −1+max{r1, 2 4+α/2 ,ρ1}).”
MARKOVIAN BRIDGES: WEAK CONTINUITY AND PATHWISE CONSTRUCTIONS (2009, unknown): “The preceding proposition is proved in [18].”
Stable distributions (2011, background): “See Bertoin [2] and Kallenberg [8, Corollary 15.8].”
A Stable Marriage of Poisson and Lebesgue (2005, background): “(i) Without loss of generality, we may assume that Π is ergodic under translations; if not, we may appeal to the ergodic decomposition theorem ([11], Theorem 10.”
Asymptotic normality of the k-core in random graphs (2006, methodology): “We simplify, at least conceptually, by using the Skorokhod coupling theorem ([19], Theorem 4.”
Multivariate supOU processes (2010, methodology): “Follows from the Lévy–Itô decomposition and the usual integration theory with respect to Poisson random measures (see [27], Lemma 12.”
A convenient category for higher-order probability theory (2017, background): “Proposition 24 ([23], Lem.”
THE MULTIVARIATE supOU STOCHASTIC VOLATILITY MODEL (2013, methodology): “Follows from the Lévy-Itô decomposition and the usual integration theory with respect to Poisson random measures (see Kallenberg 2002, lemma 12.13).”
Majority bootstrap percolation on the random graph G(n,p) (2010, methodology): “By the Skorohod coupling theorem ([35], Theorem 4.”
The Bayesian Approach to Inverse Problems (2013, background): “The existence of regular conditional probability distributions is discussed in [54], Theorem 6.”
THE DENSITY OF THE ISE AND LOCAL LIMIT LAWS FOR EMBEDDED TREES (2005, background): “Then S1 is a closed subset of the separable Banach space C0(R), and is thus Polish, and so is S2 by [18], Theorem A2.”
Tree-valued Fleming–Viot dynamics with mutation and selection (2011, methodology): “Before we turn to the proof of Theorem 2, we recall the Girsanov transform for continuous semimartingales from Kallenberg (2002), Theorems 18.”
Graphons, cut norm and distance, couplings and rearrangements (2010, background): “(The representation theorem in [42] yields a representation where the label of ij is f(Xi, Xj , ξij) for some fixed function f : [0, 1]3 → X with Xi and ξjk uniform on [0, 1] and independent of each other; it is easily seen that this leads to an equivalent representation by P(K)-valued graphons W : ”