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A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set, the probability that the paths of independent random walks do not intersect, and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic ...

Introducing the heat equation and the closely related notion of harmonic functions from a probabilistic perspective, this book includes chapters on: the discrete case, random walk and the heat equation on the integer lattice, the continuous case, Brownian motion and the usual heat equation, and martingales and fractal dimension.

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A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991,  Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the non...

A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set, the probability that the paths of independent random walks do not intersect, and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic ...

Focusing on mathematical ideas rather than proofs, Introduction to Stochastic Processes provides access to important fundamentals of stochastic processes. This second edition features additional material on stochastic integration, with expanded discussion of Girsanov transformation, an introduction to the Feynman-Kac formula, and an exposition on the Black-Scholes formula with applications from the field of mathematical finance. This new editi...

An advanced treatment of random walks written for students and researchers in probability and related fields.