Limit theorems for reinforced random walks on certain trees

Probability Theory and Related Fields

Volumn 136, Issue 1, 2006, Pages 81-101

  Collevecchio, Andrea ^a  

^a UNIVERSITY OF CHIETI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745458494     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0476-x     Document Type: Article

References (22)

1. Collevecchio, A.: Limit theorems for vertex-reinforced jump processes on certain trees. Submitted (2005)
2. Collevecchio, A.: On the transience of certain processes defined on Galton-Watson trees. Ann. Probab. to appear, 2005
3. Collevecchio, A.: Once randomly-reinforced random walk. Submitted (2005)
4. Coppersmith, D., Diaconis, P.: Random walks with reinforcement. Unpublished manuscript (1987)
5. Davis, B.: Reinforced random walk. Prob. Th. Rel. Fields 84, 203-229 (1990)
6. Davis, B.: Reinforced and perturbed random walks. In: P. Révész, B. Tóth (eds.), Random walks. Vol.IX, (113-126) (Bolyai Soc. Math. Studies), 1999
7. Davis, B., Volkov, S.: Vertex-reinforced jump process on trees and finite graphs. Prob. Th. Rel. Fields 128, 42-62 (2004)
8. Davis, B., Volkov, S.: Continuous time vertex-reinforced jump processes. Prob Th. Rel. Fields 84, 281-300 (2002)
9. Diaconis, P., Rolles, S.W.W.: Bayesian analysis for reversible Markov chains. Ann. Statist, to appear, 2005
10. Durrett, R., Kesten, H., Limic, V.: Once reinforced random walk. Prob. Th. Rel. Fields 122, 567-592 (2002)
11. Feller, W.: Probability theory and its applications, VOL H. Wiley, New York, 1957
12. Merkl, F., Rolles, S.W.W.: Edge reinforced random walk on a ladder. Ann. Probab. to appear, 2005
13. Muliere, P., Secchi, P., Walker, S.G.: Urn schemes and reinforced random walks. Stochastic Processes Appl. 88, 59-78 (2000)
14. Othmer H., Stevens, A.: Aggregation, blowup, and collapse: the ABCs of taxis and reinforced random walk. SIAM J. App. Math. 57, 1044-1081 (1997)
15. Pemantle, R.: Phase transition in reinforced random walks and rwre on trees. Ann. Probab. 16, 1229-1241 (1988)
16. Pemantle, R.: Random processes with reinforcement. Preprint
17. Pemantle R., Volkov, S.: Vertex reinforced random walks on Z have finite range. Ann. Probab. 27, 1368-1388 (1999)
18. Rolles, S.W.W.: How edge-reinforced random walk arises naturally. Prob. Th. Rel. Fields 2, 243-260 (2003)
19. Rolles, S.W.W.: On the recurrence of edge-reinforced random walks on Z × G. Prob. Th. Rel. Fields to appear, (2005)
20. Sellke, T.: Reinforced random walk on the d-dimensional integer lattice. Technical report 94-26, Department of Statistics, Purdue University (1994)
21. Tarrès, P.: VRRW on Z eventually gets stuck at a set of five points. Ann. Probab. 32, 2650-2701 (2004)
22. Walker S.G., Muliere, P.: Beta-Stacy processes and a generalization of the Polya-urn scheme. Ann. Statist. 25, 1762-1780 (1997)