Random walk with heavy tail and negative drift conditioned by its minimum and final values

2013/12/11 by Vincent Bansaye, Vladimir Vatutin, Bansaye, Vincent +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1312.3306

arXiv admin note: substantial text overlap with arXiv:1307.3963

arxiv created 2013/12/11 · openalex publication_date 2013/12/11 · arxiv updated 2013/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider random walks with finite second moment which drifts to -∞ and have heavy tail. We focus on the events when the minimum and the final value of this walk belong to some compact set. We first specify the associated probability. Then, conditionally on such an event, we finely describe the trajectory of the random walk. It yields a decomposition theorem with respect to a random time giving a big jump whose distribution can be described explicitly.

Citations

• On the survival of a class of subcritical branching processes in random environment
• A functional limit convergence towards brownian excursion

Cited by

• Conditioned local limit theorems for random walks on the real line

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