Functional limit theorems for multitype branching processes and generalized Pólya urns

By Svante Janson. 2004

340 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a3295c72d8f2f741f50d28351a06370867440c03

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Citations in the corpus

Analytic urns (2004, methodology): “…models with more than two colors; see the paper of Smythe (1996) for a thorough probabilistic treatment, the works of Aldous (1991), Aldous, Flannery and Palacios (1988) for a discussion of almost sure convergence issues, and the comprehensive and independent recent studies of Janson (2004, 2005).”
Moments of Gamma type and the Brownian supremum process area (2010, background): “It is here natural to let a, b, c, d be non-negative integers, but in fact, the model can be defined (and the results below hold) for arbitrary real a, b, c, d ≥ 0, see [15; 16].”
A survey of random processes with reinforcement (2006, methodology): “te that such results were not preexisting. The development of limit laws for multitype branching process was motivated in part by applications to urn processes. In particular, the studies [Ath68] and [Jan04] of multitype limit laws were motivated respectively by the companion paper [AK68] on urn mod”
Limit theorems for triangular urn schemes (2006, methodology): “(When α < δ, such results hold by [14], see Remark 1.”
Limit distributions for large P\'{o}lya urns (2009, methodology): “5 Notice that the distribution of ξ has been given by Janson ([9]) calculating first the distribution of u1(U CT (t))for every t: u1(U CT (t)) = u S + Z(t) where Z(t) is a negative binomial distribution.”
Some exactly solvable models of urn process theory (2006, background): “Finally, a special mention is due to the works of Athreya, Karlin, and Ney [3, 4] based on an embedding into continuous time, which has the capacity of dealing with nonbalanced urn models (see also [2]); a central contribution in this area is Janson’s recent study [62].”
Simply generated trees, conditioned Galton–Watson trees, random allocations and condensation (2011, neutral): “[58].”
Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn (2009, background): “Among more recent literature on urn models and adaptive designs, there are, for instance, [3, 4, 16, 30].”
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees (2016, background): “The same condition also appears in the different but closely related context of generalized Pólya urns, see [74].”
Asymptotic normality of the k-core in random graphs (2006, neutral): “[15].”
Plane recursive trees, Stirling permutations and an urn model (2008, background): “9], [9]), which now can be described as follows: There are individuals of three types (colours).”
THE FERMAT CUBIC, ELLIPTIC FUNCTIONS, CONTINUED FRACTIONS, AND A COMBINATORIAL EXCURSION (2005, positive): “In particular, Pouyanne (following a suggestion of Janson) obtains results relative to the Yule process with k types of balls.”
A proof of a conjecture of Buck, Chan, and Robbins on the expected value of the minimum assignment (2005, methodology): “4 in [11].”