A Guide to First-Passage Processes

The basic theory presented in a way which emphasizes intuition, problem-solving and the connections with other fields.

Sidney Redner (Author)

9780521036917, Cambridge University Press

Paperback / softback, published 15 May 2007

328 pages, 91 b/w illus.
22.9 x 15.2 x 1.9 cm, 0.48 kg

'I found the author's style accessible and interesting.' Contemporary Physics

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 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. First-passage processes provide an appealing way for graduate students and researchers in physics, chemistry, theoretical biology, electrical engineering, chemical engineering, operations research and finance to understand all of these systems.

Preface
Errata
1. First-passage fundamentals
2. First passage in an interval
3. Semi-infinite system
4. Illustrations of first passage in simple geometries
5. Fractal and nonfractal networks
6. Systems with spherical symmetry
7. Wedge domains
8. Applications to simple reactions
References
Index.

Subject Areas: Stochastics [PBWL], Applied mathematics [PBW], Finance [KFF]