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Convergence of the derivative martingale for the branching random walk in time-inhomogeneous random environment

Consider a branching random walk on the real line with a random environment in time (BRWRE). A necessary and sufficient condition for the non-triviality of the limit of the derivative martingale is formulated. To this end, we investigate the random walk in time-inhomogeneous random environment (RWRE), which related the BRWRE by the many-to-one formula. The key step is to figure out Tanaka's decomposition for the RWRE conditioned to stay non-negative (or above a line), which is interesting itself as well.

preprint2023arXivOpen access
Wenming HongShengli Liang
math.PR
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Open access2 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Wenming HongShengli Liang

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