Titlebook: Random Walk, Brownian Motion, and Martingales; Rabi Bhattacharya,Edward C. Waymire Textbook 2021 Springer Nature Switzerland AG 2021 Stoch

Fibrin

Multidimensional Random Walk,es a role for dimension . in distinguishing between recurrent and transient properties of the random walk. Namely, it is shown by combinatorial methods that the simple symmetric random walk on the .-dimensional integer lattice . is recurrent for .?=?1, 2 and transient for .?≥?3.

鑲嵌細(xì)工

,Growth of Supercritical Bienaymé–Galton–Watson Simple Branching Processes,its more detailed description of the genealogy. For a given single progenitor the tree graph structure then makes it possible to uniquely trace any given progeny to its root. A natural distance between trees is also introduced that makes the collection of all such family trees a complete and compact metric space.

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