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

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

2006-12-12

arxiv.org/abs/math/0612306v1

Mathematics

Probability

Scientific paper

Let $(Y_n)$ be a sequence of i.i.d. real valued random variables. Reflected
random walk $(X_n)$ is defined recursively by $X_0=x \ge 0$, $X_{n+1} = |X_n -
Y_{n+1}|$. 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.

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