Generalized Polya urns via stochastic approximation

F. Eggenberger, G. Pólya: Über die Statistik verketteter Vorgänge , Zeit. Angew. Math. Mech. 3

1923

Earlier work this paper cites.

H. Robbins, S. Monro: A stochastic approximation method , Ann. Math. Statist. 22

1951

Earlier work this paper cites.

D. Freedman: Bernard Friedman’s urn , Ann. Math. Statist., 36

1965

Earlier work this paper cites.

K. B. Athreya, S. Karlin: Embedding of urn schemes into continuous time Markov branching processes and related limit theorems , Ann. Math. Statist., 39

1968

Earlier work this paper cites.

N. Johnsson, S. Kotz: Urn models and their application. An approach to modern discrete probability theory . Wiley (1977)

1977

Earlier work this paper cites.

B. Hill, D. Lane, W. Sudderth: A strong law for some generalized urn processes , Ann. Probab., 8

1980

Earlier work this paper cites.

R. Pemantle: Random processes with reinforcement , Doctoral Dissertation. M.I.T. (1988)

1988

Earlier work this paper cites.

R. Gouet: A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model , Statist. Probab. Lett., 8

1989

Cited alongside, same era.

R. Pemantle. Nonconvergence to unstable points in urn models and stochastic approximations , Ann. Probab., 18

1990

Cited alongside, same era.

R. Pemantle. When are touchpoints limits for generalized Pólya urns? , Proc. Amer. Math. Soc., 113

1991

Cited alongside, same era.

P. Billingsley: Probability and Measure , 3rd ed. Wiley Series in Probability and Mathematical Statistics (1995)

1995

Cited alongside, same era.

M. Benaïm: Dynamics of stochastic approximation algorithms , Séminaire de Probabilités. Lectures Notes in Mathematics, 1709

1999

Cited alongside, same era.

M. Chen, C. Wei: A new urn model , J. Appl. Probab. 42

2005

Later among the works it cites.

S. Janson: Limit theorems for triangular urn schemes , Probab. Theory Related Fields, 134

2006

Later among the works it cites.

R. Pemantle: A survey of random processes with reinforcement , Probab. Surv., 4

2007

Later among the works it cites.

R. Argiento, R. Pemantle, B. Skyrms, S. Volkov: Learning to signal: analysis of a micro-level reinforcement model . Preprint (2008), 19 pages. To appear in Stoch. Proc. Appl

2008

Later among the works it cites.

V. Borkar: Stochastic approximation. A dynamical systems viewpoint , Cambridge University Press, (2008)

2008

Later among the works it cites.

H. M. Mahmoud: Pólya urn models , CRC Press (2009)