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About 10,000 papers for “Branching process”

Branching Process Models

2013

We consider an exponentially growing cell populations modeled as a multi-type branching process in which type i cells are those with i ≥ 0 mutations and we let Zi(t) be the number of type i cells at time t. Type i cells give birth at rate ai and die at rate bi, where the growth rate λi = ai − bi> 0. Thinking of cancer we will usually restrict our attention to the case in which i → λi is increasing, but we will see an application later in the chapter with λ1 < λ0. To take care of mutations we suppose that individuals of type i in addition give birth at rate ui+1 to individuals of type i + 1. This is slightly different than the approach of having mutations with probability ui+1 at birth, which translates into a mutation rate of aiui+1, and this must be kept in mind when comparing results. sec:bp 1 Branching process results The number of type-0 cells, Z0(t), is a branching process. Since each initial individual gives rise to an independent copy of the branching process we will suppose throughout this section that Z0(0) = 1. We begin by computing the extinction probability,

Cited by 0

Random branching process

Wolfram, Stephen · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011

Starting from a point at the center, each branch splits into two with a certain probability. Branching processes like this one are common models in many areas

Cited by 0

Coloured maximal branching process

Ozgur Aydogmus, Ozgur Aydogmus, Arka Ghosh et al. · Теория вероятностей и ее применения · 2014

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Cited by 0Open access

The collision branching process

Anyue Chen, P. K. Pollett, Hanjun Zhang et al. · Journal of Applied Probability · 2004

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Cited by 17

Records and branching process

Ahsanullah, Mohammad, Yanev, George P · CERN Document Server (European Organization for Nuclear Research) · 2009

Cited by 0

A branching process with disasters

Norman Kaplan, Aidan Sudbury, Trygve Nilsen · Journal of Applied Probability · 1975

A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.

Cited by 43

The biased annihilating branching process

Claudia Neuhauser, Aidan Sudbury · Advances in Applied Probability · 1993

In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution v λ /(λ +1) , the product measure with density λ/(1 +λ). It is shown that v λ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is v λ /(λ +1) provided the initial measure converges.

Cited by 13