Extreme order statistics of random walks

2020/07/28 by Jim Pitman, Wenpin Tang, Pitman, Jim +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F17 #60G50 #60J05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2007.13991

openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed descriptions of the limit process are given in the case of simple symmetric walks and Gaussian walks. Some open problems are also presented.

Citations

• Tables for Computing Bivariate Normal Probabilities

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