Abstract
We consider a branching random walk on ℝ with a random environment in time (denoted by ξ). Let Z n be the counting measure of particles of generation n, and let \(\tilde Z_n (t)\) be its Laplace transform. We show the convergence of the free energy n −1log \(\tilde Z_n (t)\), large deviation principles, and central limit theorems for the sequence of measures {Z n }, and a necessary and sufficient condition for the existence of moments of the limit of the martingale \(\tilde Z_n (t)/\mathbb{E}[\tilde Z_n (t)|\xi ]\).
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Huang, C., Liang, X. & Liu, Q. Branching random walks with random environments in time. Front. Math. China 9, 835–842 (2014). https://doi.org/10.1007/s11464-014-0407-1
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DOI: https://doi.org/10.1007/s11464-014-0407-1