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Reinforced and perturbed random walks. (English) Zbl 0953.60028

Révész, Pál (ed.) et al., Random walks. International workshop, Budapest, Hungary, July 13-24, 1998. Budapest: János Bolyai Mathematical Society. Bolyai Soc. Math. Stud. 9, 113-126 (1999).
Summary: This article is based on four talks given to the Workshop on Random Walks in Budapest, Hungary in July, 1998. These talks concerned some nearest neighbor walks on the integers, and the continuous processes which are their limits. In Section 1, a broad class of non-Markovian walks called reinforced random walks will be described, and the few theorems treating them in full generality will be proved, with somewhat easier arguments than the original proofs. Then results concerning special cases, including work of Rubin, Sellke, and the author will be proved, and some open problems stated. In Section 2, perturbed random walks will be briefly discussed, the brevity because the author has recently written an expository paper on this subject.
For the entire collection see [Zbl 0933.00038].

MSC:

60G50 Sums of independent random variables; random walks
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