Potential Functions of Random Walks in ¿ with Infinite Variance
Kôhei Uchiyama
Broschiertes Buch

Potential Functions of Random Walks in ¿ with Infinite Variance

Estimates and Applications

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This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems.The potential function of a random walk is a central object in...