Séminaire SPACE Tours

The reflected random walk in one and more dimensions
Judith Kloas
Friday 08 January 2016 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
The goal of this talk is to introduce the reflected random walk in higher dimensions with one or more axes of reflection and provide conditions for its recurrence behavior. The used methods are based on the works about the corresponding one-dimensional reflected random walk. It is defined by $X_0=x_0$ and $X_{n+1}=|X_n-Y_{n+1}|$, $n\geq 0$, where $Y_1,Y_2,\dotsc$ is a sequence of independent and identically distributed real valued random variables. We give a summary of some interesting results about this stochastic process, which was described and studied among others by Feller, Spitzer, Peign\'e and Woess, Boudiba and Rabeherimanana. Moreover, we want to discuss the connection between the recurrence behavior of the reflected random walk and its underlying random walk $S_n=Y_1+\dots +Y_n$. We present a surprising example, where $S_n$ is recurrent, but the corresponding reflected random walk is transient. After defining the reflected random walk in higher dimensions we give first results regarding its recurrence behavior. We conclude with a discussion of open problems and similar processes.

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