Asymptotic Results for some Preferential Attachment Models with Random Weights
ABSTRACT:
ABSTRACT:
Various asymptotic results will be shown for the "randomly reinforced" versions of
three popular models: Polya urn, Poisson-Dirichlet sequence and Indian buffet process.
The main central limit theorem will be stated for an arbitrary sequence of real random variables. Indeed, although this result has been thought for urn problems, it deals with the general problem of the rate of convergence of predictive distributions and empirical distributions for dependent data.
three popular models: Polya urn, Poisson-Dirichlet sequence and Indian buffet process.
The main central limit theorem will be stated for an arbitrary sequence of real random variables. Indeed, although this result has been thought for urn problems, it deals with the general problem of the rate of convergence of predictive distributions and empirical distributions for dependent data.
The main references are:
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"A central limit theorem and its applications to multicolor randomly reinforced urns", J. Appl. Probab., 48(2), 527-546
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"Central limit theorems for multicolor urns with dominated colors",
Stochastic Processes and their Applications, 120(8), 1473-1491
- F. Bassetti - I. Crimaldi - F. Leisen,
"Conditionally identically distributed species sampling sequences",
Adv. Appl. Probab., 42(2), 433-459
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"Central limit theorems for an Indian buffet model with random weights",
forthcoming in Annals of Applied Probability
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"A central limit theorem and its applications to multicolor randomly reinforced urns", J. Appl. Probab., 48(2), 527-546
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"Central limit theorems for multicolor urns with dominated colors",
Stochastic Processes and their Applications, 120(8), 1473-1491
- F. Bassetti - I. Crimaldi - F. Leisen,
"Conditionally identically distributed species sampling sequences",
Adv. Appl. Probab., 42(2), 433-459
- P. Berti - I. Crimaldi - L. Pratelli - P. Rigo,
"Central limit theorems for an Indian buffet model with random weights",
forthcoming in Annals of Applied Probability
Alessandra Bianchi
Dip. di Matematica Pura e Applicata
Università di Padova
Via Trieste, 63 - 35121 Padova, Italy
phone: +39 049 827 14 06
fax: +39 049 827 14 28
e-mail: bianchi@math.unipd.it
http://www.math.unipd.it/~bianchi/