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

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The Simple Random Walk I: Associated Boundary Value Distributions, Transience, and Recurrence,e combinatorics are provided in the computation of its distribution. Two possible characteristic long-time properties, (point) recurrence and transience, are identified in the course of the analysis. Recurrence is a form of “stochastic periodicity” in which the process revisits a state (or arbitrari

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Multidimensional Random Walk,ich at each step the random walk moves with equal probability to one of its 2. neighboring states on the lattice. A celebrated theorem of Pólya provides a role for dimension . in distinguishing between recurrent and transient properties of the random walk. Namely, it is shown by combinatorial method

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,Bienaymé–Galton–Watson Simple Branching Process and Extinction,vely and independently generated according to a given offspring distribution, starting from a non-negative integer number of initial .. progenitors. The state zero, referred to as extinction, is an absorbing state for the process. In this chapter a celebrated formula for the probability of extinctio

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