A Guide to First-Passage Processes

A Guide to First-Passage Processes by Sidney Redner

Title: A Guide to First-Passage Processes
Author: Sidney Redner
ISBN10: 0521652480
ISBN13: 978-0521652483
Publisher: Cambridge University Press; 1 edition (August 6, 2001)
Language: English
Subcategory: Mathematics
Size PDF: 1836 kb
Size Fb2: 1821 kb
Rating: 4.4/5
Votes: 434
Pages: 328 pages
Other Format: lit mbr doc lrf

A Guide to First-Passage Processes by Sidney Redner


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First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing, and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a modern presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems, and the kinetics of diffusion-controlled reactions. Examples discussed include neuron dynamics, self-organized criticality, kinetics of spin systems, and stochastic resonance.