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Random Walk: A Modern Introduction

Random Walk: A Modern IntroductionGregory F. Lawler and Vlada LimicContentsPrefacepage61 Basic Continuous-time Random Other Other Filtrations and strong Markov A word about constants212 Local Central Limit Characteristic Functions and Characteristic functions of Random variables Characteristic functions of Random variables LCLT characteristic function Exponential Some corollaries of the LCLT combinatorial Stirling s formula and LCLT for Poisson and continuous-time walks563 Approximation by Brownian Construction of Brownian Skorokhod Higher An alternative formulation724 Green s Recurrence and Green s generating Green s function, transient Asymptotics under weaker Potential Two Asymptotics under weaker One Fundamental Green s function for a set965 One-dimensional Gambler s ruin General One-dimensional killed Hitting a half-line1156 Potential Dirichlet Difference estimates and Harnack Further Capacity, transient Capacity in two Neumann Beurling Eigenvalue of a set1577 Dyadic Some Quantile The dyadic Proof of Theorem Higher Coupling the exit

Random walk – the stochastic process formed by successive summation of independent, identically distributed random variables – is one of the most basic and well-studied topics in probability theory. For random walks on the integer lattice Zd, the main reference is the classic book by Spitzer [16].

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