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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.
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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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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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Discounted branching random walks
Advances in Applied Probability, 1985Let F(·) be a c.d.f. on [0,∞), f(s) = ∑∞0pjsi a p.g.f. with p0 = 0, < 1 < m = Σjpj < ∞ and 1 < ρ <∞. For the functional equation for a c.d.f. H(·) on [0,∞] we establish that if 1 – F(x) = O(x–θ) for some θ > α =(log m)/(log p) there exists a unique solution H(·) to (∗) in the class C of c.d.f.’s satisfying 1 – H(x) = o(x–α).We give a
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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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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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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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Catalytic branching random walk with semi-exponential increments
Mathematical Population Studies, 2021Ekaterina Vl Bulinskaya
exaly
Application to Branching Random Walk
2016The purpose of this chapter is two-fold. First, we obtain a criterion for uniform integrability of intrinsic martingales \((W_{n})_{n\in \mathbb{N}_{0}}\) in the branching random walk as a corollary to Theorem 2.1.1 that provides a criterion for the a.s. finiteness of perpetuities.
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Branching Random Walks with Selection
2015We have studied so far various asymptotic properties of the branching random walk by means of the spinal decomposition theorem. We are now facing at two very short chapters where the branching random walk intervenes in more complicated models; these topics are close to my current research work.
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