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A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes [article]

Sophie Hautphenne, Stefano Massei
2020 arXiv   pre-print
We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton--Watson branching processes.  ...  This algorithm is based on a particular discretization of a well-known functional equation that characterizes the quasi-stationary distribution of these processes.  ...  Quasi-stationary distributions of stochastic processes have been a focus of attention for many years.  ... 
arXiv:1901.10375v2 fatcat:hqgt5xdqtnezzesqxcfndjjoqa

Random self-similar trees: A mathematical theory of Horton laws

Yevgeniy Kovchegov, Ilya Zaliapin
2020 Probability Surveys  
The Horton laws originated in hydrology with a 1945 paper by Robert E. Horton, and for a long time remained a purely empirical finding.  ...  Attempts to build a mathematical foundation behind the Horton laws during the 1990s revealed their close connection to the operation of pruning -erasing a tree from the leaves down to the root.  ...  We would like to thank Amir Dembo for providing valuable feedback, including the very idea of writing this survey; Jim Pitman for his comments and suggesting relevant publications; and Tom Kurtz for his  ... 
doi:10.1214/19-ps331 fatcat:yy333bgrlzcp7lvdtcqzttg5sq

Master Index Volumes 1-100

2002 Stochastic Processes and their Applications  
, Convergence of quasi-stationary distributions in birthdeath processes 18 (1984) 301 Keilson, J., Ramaswamy, R., The bivariate maximum process and quasi-stationary structure of birth-death processes 22  ...  Branching processes; Some convergence theorems for a supercritical Galton-Watson process 18 (1984) 188 Kotelenez, P., Continuity properties of Hilbert space valued martingales 17 (1984) 115 Kotelenez,  ...  ., A CLT for the periodograms of a r * -mixing random field 60 (1995) 313 Miller, D.R., A continuity theorem and some counterexamples for the theory of maintained systems 5 (1977) 307 Miller, D.R., Limit  ... 
doi:10.1016/s0304-4149(02)00154-0 fatcat:5zmghyapt5d5fp272vy3x63bbq

Fourteenth Conference on Stochastic Processes and their Applications

1985 Stochastic Processes and their Applications  
A typical example of stochastic differential equations is of the form dX, = a(X,) dB, + a(X,) dt, where {X,} is an R'-valued sample continuous process and {B,} is an Rd-valued Wiener process.  ...  A simple coupling argument is used to construct a sequence of general stochastic epidemics, indexed by the initial number of susceptibles, from a time-homogeneous birth-and-death process.  ...  The Influence Function and an Asymptotic Theory for Estimation in Markov Processes H. Kiinsch, ETH-Zentrum, Ziirich, Switzerland  ... 
doi:10.1016/0304-4149(85)90039-0 fatcat:vzbbjicirzeobojxq3p3mo32sy

Some stochastic models for structured populations : scaling limits and long time behavior [article]

Vincent Bansaye
2017 arXiv   pre-print
In each case, we insist on the specific techniques for the proof of convergence and for the study of the limiting model. The limiting processes offer different models of mutation-selection dynamics.  ...  In 1 particular, we finely study a process for parasite infection and the trait is the parasite load.  ...  Scaling limits In this section, we obtain the CSBP as a scaling limit of Galton-Watson processes.  ... 
arXiv:1506.04165v2 fatcat:6rxfkixzdbd23n2fjtngytj6su

On Fitting Finite Dirichlet Mixture Using ECM and MML [chapter]

Nizar Bouguila, Djemel Ziou
2005 Lecture Notes in Computer Science  
Fluid queue models play a vital role in the performance analysis of computer and telecommunication networks.  ...  The system is analysed for different active periods corresponding to the service time of an M/G/1 queue and the busy period of an M/G/1 queue.  ...  In particular, the result provides a description of the scaling limit of the simple random walks associated with the family trees of Galton-Watson processes with a finite variance offspring distribution  ... 
doi:10.1007/11551188_19 fatcat:gtzi5u6emvfyxea3zbklobnvom

The method of quasilikelihood [article]

Yan-Xia Lin, University, The Australian National, University, The Australian National
They have being developed and studied for a long time, and they still play an important role in statistics.  ...  The methods of " Maximum Likelihood " (ML) and " Least Squares" (LS) are two central methods in the theory of inference.  ...  where a simple illustration of the methodology take the case where {Xt} is a subcritical Bienayme-Galton-Watson branching process with immigration and 9' = (m, A) is to be estimated on the basis of data  ... 
doi:10.25911/5d70f2f6ddc76 fatcat:en6fdxdzvrfqnbozkk5oq34pdu