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- W4313594119 abstract "Given a super-critical branching random walk {Zn}n≥0 on R, let Zn(A) be the number of particles located in some Borel set A⊂R at generation n. Under some mild conditions, it's well-known (e.g., [4]) that Zn(nA)/Zn(R) converges almost surely to ν(A) as n→∞, where ν(⋅) is the standard Gaussian measure on R. Large deviation probabilities of Zn(nA)/Zn(R) have been well studied (see [10] and [27]). In this work, we investigate its moderate deviation probabilities, i.e. the convergence rate ofP(Zn(nA)/Zn(R)≥ν(A)+Δn) as n→∞, where {Δn}n≥0 is some positive sequence tending to zero." @default.
- W4313594119 created "2023-01-06" @default.
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- W4313594119 date "2023-07-01" @default.
- W4313594119 modified "2023-09-26" @default.
- W4313594119 title "Moderate deviation probabilities for empirical distribution of the branching random walk" @default.
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- W4313594119 doi "https://doi.org/10.1016/j.jmaa.2022.126989" @default.
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