The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Amir, G.; Benjamini, I. Kozma, G. Excited random walk against a wall. Probab. Theory Related Fields 140 (2008), no. 1-2, 83--102. MR2357671
  2. Antal, T.; Redner, S. The excited random walk in one dimension. J. Phys. A 38 (2005), no. 12, 2555--2577. MR2132073
  3. Athreya, K. B.; Ney, P. E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040
  4. Basdevant, A.-L.; Singh, A.. On the speed of a cookie random walk. Probab. Theory Related Fields 141 (2008), no. 3-4, 625--645. MR2391167
  5. Basdevant, A.-L.; Singh, A.. Rate of growth of a transient cookie random walk. Electron. J. Probab. 13 (2008), no. 26, 811--851. MR2399297
  6. Benjamini, I.; Wilson, D. B. Excited random walk. Electron. Comm. Probab. 8 (2003), 86--92 (electronic). MR1987097
  7. Bérard, J.; Ramírez, A.. Central limit theorem for the excited random walk in dimension D≥2. Electron. Comm. Probab. 12 (2007), 303--314 (electronic). MR2342709
  8. Bertoin, J.. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564
  9. Chi, Z.. Limit laws of estimators for critical multi-type Galton-Watson processes. Ann. Appl. Probab. 14 (2004), no. 4, 1992--2015. MR2099660
  10. Harris, Th. E. The theory of branching processes. Die Grundlehren der Mathematischen Wissenschaften, Bd. 119 Springer-Verlag, Berlin; Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963 xiv+230 pp. MR0163361
  11. Kosygina, E.; Zerner, M. P. W. Positively and negatively excited random walks on integers, with branching processes. Electron. J. Probab. 13 (2008), no. 64, 1952--1979. MR2453552
  12. Kozma, G. Excited random walk in three dimensions has positive speed. Preprint (2003), math.PR/0310305
  13. Kozma, G. Excited random walk in two dimensions has linear speed. Preprint (2005), math.PR/0512535
  14. Lyons, R.; Pemantle, R.; Peres, Y.. Biased random walks on Galton-Watson trees. Probab. Theory Related Fields 106 (1996), no. 2, 249--264. MR1410689
  15. Lyons, R.; Pemantle, R.; Peres, Y.. Unsolved problems concerning random walks on trees. Classical and modern branching processes (Minneapolis, MN, 1994), 223--237, IMA Vol. Math. Appl., 84, Springer, New York, 1997. MR1601753
  16. Menshikov, M. V.; Volkov, S. E. Branching Markov chains: qualitative characteristics. Markov Process. Related Fields 3 (1997), no. 2, 225--241. MR1468175
  17. Mountford, T.; Pimentel, L. P. R.; Valle, G.. On the speed of the one-dimensional excited random walk in the transient regime. ALEA Lat. Am. J. Probab. Math. Stat. 2 (2006), 279--296 (electronic). MR2285733
  18. Müller, S.. Recurrence for branching Markov chains. Electron. Commun. Probab. 13 (2008), 576--605. MR2461533
  19. Seneta, E. Nonnegative matrices and Markov chains. Second edition. Springer Series in Statistics. Springer-Verlag, New York, 1981. xiii+279 pp. ISBN: 0-387-90598-7 MR0719544
  20. Seneta, E.; Vere-Jones, D. On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. J. Appl. Probability 3 1966 403--434. MR0207047
  21. van der Hofstad, R.; Holmes, M. An expansion for self-interacting random walks. Preprint (2007), abs/0706.0614v3
  22. van der Hofstad, R.; Holmes, M. Monotonicity for excited random walk in high dimensions. To appear in Probab. Theory Related Fields (2009), abs/0803.1881
  23. Vere-Jones, D. Ergodic properties of nonnegative matrices. I. Pacific J. Math. 22 1967 361--386. MR0214145
  24. Volkov, S.. Excited random walk on trees. Electron. J. Probab. 8 (2003), no. 23, 15 pp. (electronic). MR2041824
  25. Zerner, M. P. W. Multi-excited random walks on integers. Probab. Theory Related Fields 133 (2005), no. 1, 98--122. MR2197139
  26. Zerner, M. P. W. Recurrence and transience of excited random walks on Zd and strips. Electron. Comm. Probab. 11 (2006), 118--128 (electronic). MR2231739


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.