naa a22 4500 510812155 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060047 doi (NATIONALLICENCE)springer-10.1134/S0081543813060047 Snakes and perturbed random walks [Elektronische Daten] [Gopal Basak, Stanislav Volkov] We study some properties of random walks perturbed at extrema, which are generalizations of the walks considered, e.g., by Davis (1999) and Tóth (1996). This process can also be viewed as a version of an excited random walk, recently studied by many authors. We obtain several properties related to the range of the process with infinite memory and prove the strong law, the central limit theorem, and the criterion for the recurrence of the perturbed walk with finite memory. We also state some open problems. Our methods are predominantly combinatorial and do not involve complicated analytic techniques. Pleiades Publishing, Ltd., 2013 Basak Gopal Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 700108, Kolkata, India aut Volkov Stanislav Department of Mathematics, University of Bristol, BS8 1TW, Bristol, UK aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 35-44 0081-5438 282:1<35 2013 282 11501 https://doi.org/10.1134/S0081543813060047 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060047 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Basak Gopal Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 700108, Kolkata, India aut NATIONALLICENCE 700 1- Volkov Stanislav Department of Mathematics, University of Bristol, BS8 1TW, Bristol, UK aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 35-44 0081-5438 282:1<35 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer