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References
- Angel, Omer; Crawford, Nicholas; Kozma, Gady. Localization for linearly edge reinforced random walks. Duke Math. J. 163 (2014), no. 5, 889--921. MR3189433
- Benaim, Michel. A dynamical system approach to stochastic approximations. SIAM J. Control Optim. 34 (1996), no. 2, 437--472. MR1377706
- Benaim, Michel; Raimond, Olivier; Schapira, Bruno. Strongly vertex-reinforced-random-walk on a complete graph. ALEA Lat. Am. J. Probab. Math. Stat. 10 (2013), no. 2, 767--782. MR3125746
- Benveniste, Albert; Métivier, Michel; Priouret, Pierre. Adaptive algorithms and stochastic approximations. Translated from the French by Stephen S. Wilson. Applications of Mathematics (New York), 22. Springer-Verlag, Berlin, 1990. xii+365 pp. ISBN: 3-540-52894-6 MR1082341
- Durrett, Rick. Probability: theory and examples. Fourth edition. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. x+428 pp. ISBN: 978-0-521-76539-8 MR2722836
- Kiefer, J.; Wolfowitz, J. Stochastic estimation of the maximum of a regression function. Ann. Math. Statistics 23, (1952). 462--466. MR0050243
- Kovchegov, Yevgeniy. Multi-particle processes with reinforcements. J. Theoret. Probab. 21 (2008), no. 2, 437--448. MR2391254
- Kushner, Harold J.; Clark, Dean S. Stochastic approximation methods for constrained and unconstrained systems. Applied Mathematical Sciences, 26. Springer-Verlag, New York-Berlin, 1978. x+261 pp. ISBN: 0-387-90341-0 MR0499560
- Limic, Vlada. Attracting edge property for a class of reinforced random walks. Ann. Probab. 31 (2003), no. 3, 1615--1654. MR1989445
- Limic, Vlada; Tarrès, Pierre. Attracting edge and strongly edge reinforced walks. Ann. Probab. 35 (2007), no. 5, 1783--1806. MR2349575
- Ljung, Lennart. Analysis of recursive stochastic algorithms. IEEE Trans. Automatic Control AC-22 (1977), no. 4, 551--575. MR0465458
- Pemantle, Robin. Nonconvergence to unstable points in urn models and stochastic approximations. Ann. Probab. 18 (1990), no. 2, 698--712. MR1055428
- Pemantle, Robin. A survey of random processes with reinforcement. Probab. Surv. 4 (2007), 1--79. MR2282181
- Pemantle, Robin; Volkov, Stanislav. Vertex-reinforced random walk on ${\bf Z}$ has finite range. Ann. Probab. 27 (1999), no. 3, 1368--1388. MR1733153
- Robbins, Herbert; Monro, Sutton. A stochastic approximation method. Ann. Math. Statistics 22, (1951). 400--407. MR0042668
- Tarrès, Pierre. Vertex-reinforced random walk on $\Bbb Z$ eventually gets stuck on five points. Ann. Probab. 32 (2004), no. 3B, 2650--2701. MR2078554
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