Results 1 to 10 of about 2,916 (191)
A Weak Limit Theorem for Galton-Watson Processes in Varying Environments [PDF]
Journal of Applied Mathematics, 2014 We extend Donsker’s theorem and the central limit theorem of classical Galton-Watson process to the Galton-Watson processes in varying environment.
Zhenlong Gao, Yanhua Zhang
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On the Local Limit Theorem for a Critical Galton–Watson Process [PDF]
Theory of Probability and Its Applications, 2006 The proof of the local limit theorem for a critical Galton–Watson process is given under minimal moment restrictions, i.e., under the condition that there exists the second moment of the number of direct offspring of one particle.
S V Nagaev
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The Width of Galton- Watson Trees Conditioned by the Size [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ 2 are asymptotically given by (σ√ n) p m p where m p are the moments of the maximum of the local time of a standard scaled Brownian ...
Michael Drmota, Bernhard Gittenberger
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GENERALIZATION OF WATSON'S THEOREM FOR DOUBLE SERIES [PDF]
Communications of the Korean Mathematical Society, 2004 Summary: In 1965, Bhatt and Pandey [Bhatt, R.C.; Pandey, R.C., Ganita 16, 89-98 (1965; Zbl 0148.05002)] obtained the Watson's theorem for double series by using Dixon's theorem on thesum of a \({}_3F_2\). The aim of this paper is to derive twenty three results for double series closely related to the Watson's theorem for double series obtained by Bhatt
Yong-Sup Kim
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A Scaling Limit Theorem for Galton–Watson Processes in Varying Environments
Proceedings of the Steklov Institute of Mathematics, 2022 We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit theorem gives rise to the continuous-state branching processes in varying environments studied recently by several ...
Jiawei Liu, Li Zenghu
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The Local Limit Theorem for the Galton-Watson Process
Annals of Probability, 1976 The usual form of local limit theorem is extended to an arbitrary supercritical Galton-Watson process with arbitrary initial distribution. The existence of a continuous density on $(0, \infty)$ for the limit random variable $W$, in the process initiated by a single ancestor, follows from the derivation.
Dubuc, S., Seneta, E.
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A Limit Theorem on a Subcritical Galton-Watson Process with Immigration
Annals of Probability, 1982 For a sub-critical Galton-Watson process $\mathbf{X}$ with immigration, estimators have been studied by Pakes (1971) for the mean of the stationary distribution of $\mathbf{X}$, and by Nanthi (1979) for the offspring mean and the immigration mean of $\mathbf{X}$. These estimators have been shown by them to be asymptotically normal.
Venkataraman, K. N., Nanthi, K.
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A limit theorem for the contour process of condidtioned Galton--Watson trees
Annals of Probability, 2003 In this work, we study asymptotics of the genealogy of Galton--Watson processes conditioned on the total progeny. We consider a fixed, aperiodic and critical offspring distribution such that the rescaled Galton--Watson processes converges to a continuous-state branching process (CSBP) with a stable branching mechanism of index $α\in (1, 2]$.
Thomas Duquesne
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Sums of quaternion squares and a theorem of Watson [PDF]
Involve, a Journal of Mathematics, 2021 We use a representability theorem of G. L. Watson to examine sums of squares in Quaternion rings with integer coefficients. This allows us to determine a large family of such rings where every element expressible as the sum of squares can be written as the sum of 3 squares.
Banks, Tim +3 more
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Subcritical pattern languages for and/or trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let $P_k(f)$ denote the density of and/or trees defining a boolean function $f$ within the set of and/or trees with fixed number of variables $k$. We prove that there exists constant $B_f$ such that $P_k(f) \sim B_f \cdot k^{-L(f)-1}$ when $k \to \infty$,
Jakub Kozik
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