On recurrence of reflected random walk on the half-line. With an appendix on results of Martin Benda

2006/12/12 by Marc Peigné, Peigné, Marc, Wolfgang Woess +1
Mathematics · #60G50 #60J05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G50 #msc:60J05

paper · pdf · doi:10.48550/arxiv.math/0612306

arxiv created 2006/12/12 · arxiv updated 2009/12/01

Abstract

Let (Y_n) be a sequence of i.i.d. real valued random variables. Reflected random walk (X_n) is defined recursively by X₀=x ≥ 0, X_n+1 = |X_n - Y_n+1|. In this note, we study recurrence of this process, extending a previous criterion. This is obtained by determining an invariant measure of the embedded process of reflections.

Related

• Return Probabilities for the Reflected Random Walk on \mathbb N₀
• Multidimensional random walk with reflections
• Limit theorem for reflected random walks
• Conditions for recurrence and transience for one family of random walks
• Recurrence of Multidimensional Persistent Random Walks. Fourier and Series Criteria