Results 121 to 130 of about 2,197 (146)

An improvement of Watson’s theorem on Borel summability

Journal of Mathematical Physics, 1980
Watson’s theorem, which gives sufficient conditions for Borel summability, is not optimal. Watson assumes analyticity and uniform asymptotic expansion in a sector ‖argz‖<π/2+ε, ‖z‖<R, with ε≳0; in fact, only the circular region Re(1/z) ≳1/R is required. In particular, one can take ε=0.
Sokal Alan D
exaly   +3 more sources

Limit Theorems for a Galton–Watson Process with Immigration in Varying Environments

Bulletin of the Malaysian Mathematical Sciences Society, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenlong Gao
exaly   +2 more sources

Limit theorem for a supercritical Galton-Watson process

Mathematical Notes, 1975
Letμ n, n = 0, 1, ..., be a Galton-Watson process, and τx + 1 the instant of first crossing of the level x by the process. A limit theorem is proved for the joint distribution of the random variables $$\tau _x ,x - \mu _{\tau _x } ,\mu _{\tau _x + 1} - x(x \to \infty )$$
exaly   +3 more sources

On a Theorem of Quine and Seneta for the Galton‐Watson Process With Immigration

The Australian Journal of Statistics, 1971
SummaryRecently a limit theorem has been obtained for the limiting‐stationary distribution of a process in which individuals reproduce as in a subcritical Galton‐Watson process and are subject to an independent immigration component at each generation. This paper provides a different proof of this theorem, and under slightly weaker conditions.
exaly   +2 more sources

The Watson Theorem Prover

Journal of Automated Reasoning, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Randall Holmes, Jim Alves-Foss
openaire   +2 more sources

A LIMIT THEOREM FOR THE GALTON‐WATSON PROCESS WITH IMMIGRATION

Australian Journal of Statistics, 1969
SummaryIt is difficult, in general, to optain an explicit expression for the limiting‐stationary distribution, when such a distribution exists, of the process in which teh individuals reproduce as in a Galton‐Wastson process, but are also subject to an independent immigration component at each generation.
Quine, M. P., Seneta, E.
openaire   +2 more sources

Limit Theorems for the Critical Galton–Watson Processes with Migration

Theory of Probability & Its Applications, 1996
Let \(\xi_i^{(n)}\), \(\zeta_n\), \(i=1,2,\dots,\;n=0,1,\dots\), be independent aleatory variables with \(P(\zeta_n=k)=p_k\), \(P(\zeta_n=-r)=q_r\), \(k=0,1,\dots,\;r=1,2,\dots,m\), \(\sum_{k=0}^\infty p_k+\sum_{r=1}^m q_r=1\), and \(\xi_i^{(n)}\), \(i=1,2,\dots,\) are independent identically distributed for every \(n=0,1,\dots\) We consider the ...
Badalbaev, I. S., Yakubov, T. D.
openaire   +2 more sources

An extension of Hawkes theorem on the Hausdorff dimension of a Galton–Watson tree

Probability Theory and Related Fields, 2000
The genealogical tree of a supercritical multi-type Galton-Watson branching process (simple Galton-Watson process assigned labels from a finite set \(\mathcal L\)) is considered. There is defined the limit set \(\Lambda\) of the simple Galton-Watson process as the set of all infinite descent lines, i.e., the set of infinite sequences \(\xi =\xi_1 \xi_2
Lalley, Steven P., Sellke, Thomas
openaire   +2 more sources

Watson's theorem and the $NΔ(1232)$ axial transition

2015
We present a new determination of the $NΔ$ axial form factors from neutrino induced pion production data. For this purpose, the model of Hernandez {\it et al.} [Phys. Rev. D76, 033005 (2007)] is improved by partially restoring unitarity. This is accomplished by imposing Watson's theorem on the dominant vector and axial multipoles.
Alvarez-Ruso, L., Hernández, E., Nieves, J., Vacas, M. J. Vicente   +3 more
openaire   +1 more source

Renewed Limit Theorems for Noncritical Galton–Watson Branching Systems

Journal of Theoretical Probability
This paper discusses the Galton-Watson stochastic branching system. The authors deal only with the noncritical case. Their goal is to improve the recent results on explicitly calculated famous constant in the theory of subcritical Galton-Watson branching systems (Kolmogorov (1938)).
Azam A. Imomov, Misliddin Murtazaev
openaire   +1 more source