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Journal articles on the topic 'Branching processes'

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Published: 4 June 2021
Last updated: 31 July 2024

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1

Nerman, Olle, S. Asmussen, and H. Hering. "Branching Processes." Journal of the American Statistical Association 81, no. 395 (September 1986): 858. http://dx.doi.org/10.2307/2289024.

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2

Krapivsky, P. L., and S. Redner. "Immortal branching processes." Physica A: Statistical Mechanics and its Applications 571 (June 2021): 125853. http://dx.doi.org/10.1016/j.physa.2021.125853.

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3

Mayster, Penka. "Alternating branching processes." Journal of Applied Probability 42, no. 4 (December 2005): 1095–108. http://dx.doi.org/10.1239/jap/1134587819.

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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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4

Mayster, Penka. "Alternating branching processes." Journal of Applied Probability 42, no. 04 (December 2005): 1095–108. http://dx.doi.org/10.1017/s0021900200001133.

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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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5

Weiss, Gideon. "Branching Bandit Processes." Probability in the Engineering and Informational Sciences 2, no. 3 (July 1988): 269–78. http://dx.doi.org/10.1017/s0269964800000826.

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A set of ni arms of type i, i = 1,…, L, is available. A pull of arm of type i occupies a duration Vi at the end of which a reward Ci and Ni1,…, NiL new arms are obtained, while all other arms are frozen. A Gittins priority order of types is obtained and shown to yield the maximal discounted reward from this branching process of arms.
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6

Bramson, Maury, Ding Wan-ding, and Rick Durrett. "Annihilating branching processes." Stochastic Processes and their Applications 37, no. 1 (February 1991): 1–17. http://dx.doi.org/10.1016/0304-4149(91)90056-i.

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7

Vatutin, V. A., and A. M. Zubkov. "Branching processes. II." Journal of Soviet Mathematics 67, no. 6 (December 1993): 3407–85. http://dx.doi.org/10.1007/bf01096272.

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8

Vatutin, V. A., and A. M. Zubkov. "Branching processes. I." Journal of Soviet Mathematics 39, no. 1 (October 1987): 2431–75. http://dx.doi.org/10.1007/bf01086176.

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9

Jagers, Peter, and Andreas Lagerås. "General branching processes conditioned on extinction are still branching processes." Electronic Communications in Probability 13 (2008): 540–47. http://dx.doi.org/10.1214/ecp.v13-1419.

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10

Li, Zenghu. "Path-valued branching processes and nonlocal branching superprocesses." Annals of Probability 42, no. 1 (January 2014): 41–79. http://dx.doi.org/10.1214/12-aop759.

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11

Rahimov, I., and B. Chanane. "Branching Processes with Incubation." Stochastic Models 24, no. 1 (February 2008): 71–88. http://dx.doi.org/10.1080/15326340701828282.

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12

Janson, Svante, Oliver Riordan, and Lutz Warnke. "Sesqui-type branching processes." Stochastic Processes and their Applications 128, no. 11 (November 2018): 3628–55. http://dx.doi.org/10.1016/j.spa.2017.12.007.

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13

Dynkin, E. B., S. E. Kuznetsov, and A. V. Skorokhod. "Branching measure-valued processes." Probability Theory and Related Fields 99, no. 1 (March 1994): 55–96. http://dx.doi.org/10.1007/bf01199590.

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14

Sagitov, Serik. "Measure-branching renewal processes." Stochastic Processes and their Applications 52, no. 2 (August 1994): 293–307. http://dx.doi.org/10.1016/0304-4149(94)90030-2.

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15

Bouzas, Antonio O. "Intermittency in branching processes." Zeitschrift für Physik C Particles and Fields 64, no. 4 (December 1994): 665–73. http://dx.doi.org/10.1007/bf01957775.

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16

Bertoin, Jean, Jean-François Le Gall, and Yves Le Jan. "Spatial Branching Processes and Subordination." Canadian Journal of Mathematics 49, no. 1 (February 1, 1997): 24–54. http://dx.doi.org/10.4153/cjm-1997-002-x.

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AbstractWe present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the Brownian snake. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.
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17

Sagitov, S. M. "General branching processes: Convergence to irzhina processes." Journal of Mathematical Sciences 69, no. 4 (April 1994): 1199–206. http://dx.doi.org/10.1007/bf01249806.

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18

Shiozawa, Yuichi. "Extinction of branching symmetric α-stable processes." Journal of Applied Probability 43, no. 4 (December 2006): 1077–90. http://dx.doi.org/10.1239/jap/1165505209.

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We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.
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19

Shiozawa, Yuichi. "Extinction of branching symmetric α-stable processes." Journal of Applied Probability 43, no. 04 (December 2006): 1077–90. http://dx.doi.org/10.1017/s0021900200002448.

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We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.
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20

Dolgopyat, D., P. Hebbar, L. Koralov, and M. Perlman. "Multi-type branching processes with time-dependent branching rates." Journal of Applied Probability 55, no. 3 (September 2018): 701–27. http://dx.doi.org/10.1017/jpr.2018.46.

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Abstract Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as time goes to ∞.
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21

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 1 (March 2000): 140–58. http://dx.doi.org/10.1239/aap/1013540027.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.
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22

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 01 (March 2000): 140–58. http://dx.doi.org/10.1017/s0001867800009812.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.
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23

Lagerås, Andreas Nordvall, and Anders Martin-Löf. "Genealogy for supercritical branching processes." Journal of Applied Probability 43, no. 4 (December 2006): 1066–76. http://dx.doi.org/10.1239/jap/1165505208.

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We study the genealogy of so-called immortal branching processes, i.e. branching processes where each individual upon death is replaced by at least one new individual, and conclude that their marginal distributions are compound geometric. The result also implies that the limiting distributions of properly scaled supercritical branching processes are compound geometric. We exemplify our results with an expression for the marginal distribution for a class of branching processes that have recently appeared in the theory of coalescent processes and continuous stable random trees. The limiting distribution can be expressed in terms of the Fox H-function, and in special cases by the Meijer G-function.
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24

Lagerås, Andreas Nordvall, and Anders Martin-Löf. "Genealogy for supercritical branching processes." Journal of Applied Probability 43, no. 04 (December 2006): 1066–76. http://dx.doi.org/10.1017/s0021900200002436.

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We study the genealogy of so-called immortal branching processes, i.e. branching processes where each individual upon death is replaced by at least one new individual, and conclude that their marginal distributions are compound geometric. The result also implies that the limiting distributions of properly scaled supercritical branching processes are compound geometric. We exemplify our results with an expression for the marginal distribution for a class of branching processes that have recently appeared in the theory of coalescent processes and continuous stable random trees. The limiting distribution can be expressed in terms of the Fox H-function, and in special cases by the Meijer G-function.
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25

Kyprianou, A. E., and J. C. Pardo. "Continuous-State Branching Processes and Self-Similarity." Journal of Applied Probability 45, no. 4 (December 2008): 1140–60. http://dx.doi.org/10.1239/jap/1231340239.

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In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.
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26

Kyprianou, A. E., and J. C. Pardo. "Continuous-State Branching Processes and Self-Similarity." Journal of Applied Probability 45, no. 04 (December 2008): 1140–60. http://dx.doi.org/10.1017/s0021900200005039.

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In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.
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27

Olofsson, Peter. "General branching processes with immigration." Journal of Applied Probability 33, no. 4 (December 1996): 940–48. http://dx.doi.org/10.2307/3214975.

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A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given.
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28

Greven, Andreas, Thomas Rippl, and Patrick Glöede. "Branching Processes - A General Concept." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 635. http://dx.doi.org/10.30757/alea.v18-25.

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29

Jagers, Peter. "Branching Processes as Population Dynamics." Bernoulli 1, no. 1/2 (March 1995): 191. http://dx.doi.org/10.2307/3318688.

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30

Lowther, Jason, and Peter Guttorp. "Statistical Inference for Branching Processes." Journal of the Operational Research Society 43, no. 11 (November 1992): 1110. http://dx.doi.org/10.2307/2584114.

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31

Panaretos, J., and P. Guttorp. "Statistical Inference for Branching Processes." Biometrics 51, no. 1 (March 1995): 383. http://dx.doi.org/10.2307/2533356.

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32

Epps, T. W. "Stock prices as branching processes." Communications in Statistics. Stochastic Models 12, no. 4 (January 1996): 529–58. http://dx.doi.org/10.1080/15326349608807400.

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33

Munford, Alan G. "Inequalities for alternating branching processes." International Journal of Mathematical Education in Science and Technology 20, no. 4 (July 1989): 575–78. http://dx.doi.org/10.1080/0020739890200412.

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34

Holzheimer, J. "On moments for branching processes." Applicationes Mathematicae 19, no. 2 (1987): 181–88. http://dx.doi.org/10.4064/am-19-2-181-188.

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35

Joffe, A., and G. Letac. "Multitype linear fractional branching processes." Journal of Applied Probability 43, no. 4 (December 2006): 1091–106. http://dx.doi.org/10.1239/jap/1165505210.

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We complete a paper written by Edward Pollak in 1974 on a multitype branching process the generating functions of whose birth law are fractional linear functions with the same denominator. The main tool is a parameterization of these functions adapted using the mean matrix M and an element w of the first quadrant. We use this opportunity to give a self-contained presentation of Pollak's theory.
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36

Piau, Didier. "Asymptotics of Iterated Branching Processes." Journal of Applied Probability 46, no. 3 (September 2009): 917–24. http://dx.doi.org/10.1239/jap/1253279859.

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Gaweł and Kimmel (1996) introduced and studied iterated Galton–Watson processes, (Xn)n≥0, possibly with thinning, as models of the number of repeats of DNA triplets during some genetic disorders. Our main results are the following. If the process indeed involves some thinning then extinction, {Xn→0}, and explosion, {Xn→∞}, can have positive probability simultaneously. If the underlying (simple) Galton–Watson process is nondecreasing with mean m then, conditionally on explosion, the ratios (log Xn+1)/Xn converge to logm almost surely. This simplifies the arguments of Gaweł and Kimmel, and confirms and extends a conjecture of Pakes (2003).
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37

Teich, M. C., and B. E. A. Saleh. "Branching processes in quantum electronics." IEEE Journal of Selected Topics in Quantum Electronics 6, no. 6 (November 2000): 1450–57. http://dx.doi.org/10.1109/2944.902200.

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38

Overbeck, Ludger. "Estimation for Continuous Branching Processes." Scandinavian Journal of Statistics 25, no. 1 (March 1998): 111–26. http://dx.doi.org/10.1111/1467-9469.00092.

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39

Lowther, Jason. "Statistical Inference for Branching Processes." Journal of the Operational Research Society 43, no. 11 (November 1992): 1110. http://dx.doi.org/10.1057/jors.1992.175.

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40

Olofsson, Peter. "General branching processes with immigration." Journal of Applied Probability 33, no. 04 (December 1996): 940–48. http://dx.doi.org/10.1017/s0021900200100373.

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A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given.
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41

Kingman, J. F. C. "Random dissections and branching processes." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 1 (July 1988): 147–51. http://dx.doi.org/10.1017/s0305004100065324.

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For a time in the mid-1970s probabilists were tantalized by a seemingly simple problem posed by Araki and Kakutani[3]. An interval is repeatedly divided by points chosen successively at random, the nth point being uniformly distributed over the largest of the n intervals formed by the first n − 1 points. Is this sequence of points asymptotically uniformly distributed?
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42

Joffe, A., and G. Letac. "Multitype linear fractional branching processes." Journal of Applied Probability 43, no. 04 (December 2006): 1091–106. http://dx.doi.org/10.1017/s002190020000245x.

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Abstract:
We complete a paper written by Edward Pollak in 1974 on a multitype branching process the generating functions of whose birth law are fractional linear functions with the same denominator. The main tool is a parameterization of these functions adapted using the mean matrix M and an element w of the first quadrant. We use this opportunity to give a self-contained presentation of Pollak's theory.
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43

Piau, Didier. "Asymptotics of Iterated Branching Processes." Journal of Applied Probability 46, no. 03 (September 2009): 917–24. http://dx.doi.org/10.1017/s0021900200005957.

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Gaweł and Kimmel (1996) introduced and studied iterated Galton–Watson processes, (X n ) n≥0, possibly with thinning, as models of the number of repeats of DNA triplets during some genetic disorders. Our main results are the following. If the process indeed involves some thinning then extinction, {X n →0}, and explosion, {X n →∞}, can have positive probability simultaneously. If the underlying (simple) Galton–Watson process is nondecreasing with mean m then, conditionally on explosion, the ratios (log X n+1 )/X n converge to logm almost surely. This simplifies the arguments of Gaweł and Kimmel, and confirms and extends a conjecture of Pakes (2003).
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44

Maâouia, Faı̈za, and Abderrahmen Touati. "Identification of multitype branching processes." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 331, no. 11 (December 2000): 923–28. http://dx.doi.org/10.1016/s0764-4442(00)01741-9.

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45

RIORDAN, OLIVER. "Thek-Core and Branching Processes." Combinatorics, Probability and Computing 17, no. 1 (January 2008): 111–36. http://dx.doi.org/10.1017/s0963548307008589.

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Thek-coreof a graphGis the maximal subgraph ofGhaving minimum degree at leastk. In 1996, Pittel, Spencer and Wormald found the threshold λcfor the emergence of a non-trivialk-core in the random graphG(n, λ/n), and the asymptotic size of thek-core above the threshold. We give a new proof of this result using a local coupling of the graph to a suitable branching process. This proof extends to a general model of inhomogeneous random graphs with independence between the edges. As an example, we study thek-core in a certain power-law or ‘scale-free’ graph with a parameterccontrolling the overall density of edges. For eachk≥ 3, we find the threshold value ofcat which thek-core emerges, and the fraction of vertices in thek-core whencis ϵ above the threshold. In contrast toG(n, λ/n), this fraction tends to 0 as ϵ→0.
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46

Mitov, Georgi K., Kosto V. Mitov, and Nikolay M. Yanev. "Critical randomly indexed branching processes." Statistics & Probability Letters 79, no. 13 (July 2009): 1512–21. http://dx.doi.org/10.1016/j.spl.2009.03.010.

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47

Li, Junping, and Anyue Chen. "Generalized Markov interacting branching processes." Science China Mathematics 61, no. 3 (July 5, 2017): 545–62. http://dx.doi.org/10.1007/s11425-016-0341-4.

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48

Bai, S. Kalpana, and T. M. Durairajan. "Estimating functions for branching processes." Journal of Statistical Planning and Inference 53, no. 1 (August 1996): 21–32. http://dx.doi.org/10.1016/0378-3758(95)00149-2.

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49

Basawa, Ishwar V. "Statistical inference for branching processes." Journal of Statistical Planning and Inference 47, no. 3 (October 1995): 393–94. http://dx.doi.org/10.1016/0378-3758(95)90027-6.

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50

Jagers, Peter. "Branching processes as Markov fields." Stochastic Processes and their Applications 26 (1987): 189. http://dx.doi.org/10.1016/0304-4149(87)90076-7.

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