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Branching Random Walks with Immigration
2017The paper contains several results on the existence of limits for the first two moments of the popular model in the population dynamics: continuous-time branching random walks on the multidimensional lattice \(\mathbb Z^d\), \(d\ge 1\), with immigration and infinite number of initial particles.
Dan Han +3 more
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Branching random walk with a critical branching part
Journal of Theoretical Probability, 1995Let \(M_n\) be the maximal displacement of a branching random walk, where the offspring distribution has finite variance and mean 1 and the increments of the random walk have \((4 + \varepsilon)\)-th finite moment and mean zero. Let \(\beta>0\). The main result is that \(n^{-1/2}M_n\) conditioned on nonextinction till time \(n \beta\) of the branching ...
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2015
I Introduction.- II Galton-Watson trees.- III Branching random walks and martingales.- IV The spinal decomposition theorem.- V Applications of the spinal decomposition theorem.- VI Branching random walks with selection.- VII Biased random walks on Galton-Watson trees.- A Sums of i.i.d. random variables.- References.
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I Introduction.- II Galton-Watson trees.- III Branching random walks and martingales.- IV The spinal decomposition theorem.- V Applications of the spinal decomposition theorem.- VI Branching random walks with selection.- VII Biased random walks on Galton-Watson trees.- A Sums of i.i.d. random variables.- References.
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2014
In this chapter we consider a continuous time spatial branching process. Births and deaths are as in the binary branching process. In addition we keep track of the spatial location of the particles. We use results about the binary branching process.
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In this chapter we consider a continuous time spatial branching process. Births and deaths are as in the binary branching process. In addition we keep track of the spatial location of the particles. We use results about the binary branching process.
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Stochasticity, invasions, and branching random walks
Theoretical Population Biology, 2004We link deterministic integrodifference equations to stochastic, individual-based simulations by means of branching random walks. Using standard methods, we determine speeds of invasion for both average densities and furthest-forward individuals.
Mark, Kot +3 more
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2010
A branching random walk is a branching tree such that with each line of descent a random walk is associated. This paper provides some results on the asymptotics of the point processes generated by the positions of the nth generation individuals. An application to the photon–electron energy cascade is also given.
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A branching random walk is a branching tree such that with each line of descent a random walk is associated. This paper provides some results on the asymptotics of the point processes generated by the positions of the nth generation individuals. An application to the photon–electron energy cascade is also given.
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1991
In a volume dedicated to Ted Harris, it is appropriate that there should be some discussion of branching processes, a subject of which he is one of the founders. In a series of papers in the 1940’s and 50’s (see references [1] to [9] at the end of this paper), culminating in his famous 1963 book “The Theory of Branching Processes” [10], he helped to ...
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In a volume dedicated to Ted Harris, it is appropriate that there should be some discussion of branching processes, a subject of which he is one of the founders. In a series of papers in the 1940’s and 50’s (see references [1] to [9] at the end of this paper), culminating in his famous 1963 book “The Theory of Branching Processes” [10], he helped to ...
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Branching random walks in random environment
2021We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e. random branching/killing rates). The main question is about the location where the main part of the population sits at a late time, if the state space is large. For answering this, we take the expectation with respect to the migration (
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Quasirandom Sequences in Branching Random Walks *
Monte Carlo Methods and Applications, 2004Abdujabor Rasulov +2 more
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Clustering Effect for Multitype Branching Random Walk
Theory of Probability and Its Applications, 2022exaly