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Gutiérrez C, Minuesa C. Predator–prey density-dependent branching processes. STOCH MODELS 2022. [DOI: 10.1080/15326349.2022.2032755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Cristina Gutiérrez
- Departamento de Matemáticas, Facultad de Empresa, Finanzas y Turismo, Universidad de Extremadura, Cáceres, Spain
| | - Carmen Minuesa
- Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain
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2
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A note on the local asymptotic mixed normality of a controlled branching process with a random control function. Stat Probab Lett 2022. [DOI: 10.1016/j.spl.2021.109270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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3
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González M, Minuesa C, del Puerto I. Minimum disparity estimation in controlled branching processes. Electron J Stat 2017. [DOI: 10.1214/17-ejs1232] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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4
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Abstract
The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L
1-convergence. Finally, taking into account the classical X log+
X criterion in branching processes, a necessary and sufficient condition is provided.
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5
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Abstract
We introduce the idea of controlling branching processes by means of another branching process, using the fractional thinning operator of Steutel and van Harn. This idea is then adapted to the model of alternating branching, where two Markov branching processes act alternately at random observation and treatment times. We study the extinction probability and limit theorems for reproduction by n cycles, as n → ∞.
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6
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Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.01.015] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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7
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Bruss FT, Duerinckx M. Resource dependent branching processes and the envelope of societies. ANN APPL PROBAB 2015. [DOI: 10.1214/13-aap998] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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8
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9
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Martínez R, Mota M, del Puerto I. On asymptotic posterior normality for controlled branching processes. STATISTICS-ABINGDON 2009. [DOI: 10.1080/02331880802395971] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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10
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González M, Martínez R, Mota M. OnL2-Convergence in a Class of Homogeneous Multitype Markov Chains. STOCH MODELS 2008. [DOI: 10.1080/15326340802232269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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11
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Estimation of the offspring mean in a controlled branching process with a random control function. Stoch Process Their Appl 2007. [DOI: 10.1016/j.spa.2006.11.002] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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12
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Abstract
We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.
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Abstract
In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.
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14
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González M, Martínez R, del Puerto I. Estimation of the variance for a controlled branching process. TEST-SPAIN 2005. [DOI: 10.1007/bf02595403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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15
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González M, Molina M, Del Puerto I. On L2-convergence of controlled branching processes with random control function. BERNOULLI 2005. [DOI: 10.3150/bj/1110228241] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Manuel Molina
- Department of Mathematics, University of Extremadura
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González M, Martínez R, del Puerto I. Nonparametric estimation of the offspring distribution and the mean for a controlled branching process. TEST-SPAIN 2004. [DOI: 10.1007/bf02595782] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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17
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González M, Molina M, del Puerto I. Limiting distribution for subcritical controlled branching processes with random control function. Stat Probab Lett 2004. [DOI: 10.1016/j.spl.2003.12.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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