An Introduction to the Theory of Point Processes

By Daryl J. Daley, David Vere-Jones. 2013

2,892 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “In particular, Blei and Lafferty [2006] proposed dynamic topic models (DTMs), which, given a division of text documents into time slices, attempt to fit a generative model where topics evolve over time, and documents are drawn from the topics available at the time slice during which they were publis”
Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012, background): “To explain this issue in more detail, we recall that it is proved in [20] that a stationary random measure M over Rd is almost surely non-atomic if (C stands here for the unit cube of Rd) ∀δ > 0, nP ( M(n−1C) > δ ) → 0 as n→∞.”
Self-Exciting Point Process Modeling of Crime (2011, methodology): “…which may be defined as the limiting expected rate of the accumulation of points around a particular spatial-temporal location, given the history Ht of all points up to time t (Daley and Vere-Jones 2003): λ(t, x, y) = lim t, x, y↓0 ( E [ N{(t, t + t) × (x, x + x) × (y, y + y)}|Ht ] /( t x y) ) .”
Credit risk modeling with affine processes (2007, background): “Additional sources include Daley and Vere-Jones [1988] and Karr [1991].”
Multi-Period Corporate Default Prediction With Stochastic Covariates (2007, neutral): “7 For other textbook treatments, see Andersen, Borgan, Gill, and Keiding (1992), Miller (1981), Cox and Isham (1980), Cox and Oakes (1984), Daley and Vere-Jones (1988) , and Therneau and Grambsch (2000).”
A Composite Likelihood Approach in Fitting Spatial Point Process Models (2006, methodology): “The assumption that N is ergodic is used to prove that An → λ2Kw(r; θ) almost surely in the proof of Theorem 1, where An is defined by (A.1) in Appendix A. (For a detailed discussion of this condition, see Daley and Vere-Jones 1988, pp. 330–340.)”
Extremal behavior of regularly varying stochastic processes (2005, background): “For details on ŵ-, vague- and weak convergence we refer to Daley and Vere-Jones (1988, Appendix 2). See also Kallenberg (1983) for details on vague convergence.”
Homogenization of random singular structures and random measures (2006, background): “’(!)µ (d!). (1.11) Theorem 1.1 (the ergodic theorem [ 13 ]).”