Random Walk: A Modern Introduction (Cambridge Studies in Advanced Mathematics)

Random Walk: A Modern Introduction (Cambridge Studies in Advanced Mathematics)

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Vlada Limic Gregory F. Lawler
Cambridge University Press, 6/24/2010
EAN 9780521519182, ISBN10: 0521519187

Hardcover, 376 pages, 23.5 x 15.6 x 2.3 cm
Language: English

Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

1. Introduction
2. Local central limit theorem
3. Approximation by Brownian motion
4. Green's function
5. One-dimensional walks
6. Potential theory
7. Dyadic coupling
8. Additional topics on simple random walk
9. Loop measures
10. Intersection probabilities for random walks
11. Loop-erased random walk
Index of symbols