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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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Branching random walks and their applications for epidemic modeling
Stochastic Models, 2019Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modeling, we suggest to apply branching processes with transport of particles usually called branching random walks (BRWs).
E. Ermakova +2 more
semanticscholar +3 more sources
Local times and capacity for transient branching random walks
Probability theory and related fields, 2023We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate last passage ...
A. Asselah, Bruno Schapira, Perla Sousi
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On one limit theorem for branching random walks
Teoriya Veroyatnostei i ee Primeneniya, 2023Общая теория марковских случайных процессов была заложена А. Н. Колмогоровым. К таким процессам относятся ветвящиеся случайные блуждания по решеткам $\mathbf{Z}^d$, $d\in\mathbf{N}$.
Наталия Васильевна Смородина +3 more
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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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Branching Random Walks on $Z^d$ with Periodic Branching Sources
Theory of Probability and its Applications, 2019We consider a continuous-time branching random walk on $Z^d$ with birth and death of particles at a periodic set of points (the sources of branching).
M. Platonova, K. S. Ryadovkin
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A note on large deviation probabilities for empirical distribution of branching random walks
Statistics and Probability Letters, 2019We consider a branching random walk on R started from the origin. Let Z n ( ⋅ ) be the counting measure which counts the number of individuals at the n th generation located in a given set. For any interval A ⊂ R , it is well known that Z n ( n A ) Z n (
Wan-Xiong Shi
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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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