Long runs under point conditioning. The real case

2010/10/18 by Michel Broniatowski, Broniatowski, Michel, Virgile Caron +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Primary 60G50 #Probabilistic and Robust Engineering Design #Probability (math.PR) #Simulation Techniques and Applications #Statistical Distribution Estimation and Applications #secondary 65C50

paper · pdf · doi:10.48550/arxiv.1010.3616

openalex publication_date 2010/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or large deviation type. The result extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An algorithm for the simulation of such long runs is presented, together with an algorithm determining their maximal length for which the approximation is valid up to a prescribed accuracy.

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• Long runs under a conditional limit distribution

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