Nonlinear and unbalanced urn models with two types of strategies: a stochastic approximation point of view

被引：0
作者：
Idriss, Soumaya [1 ]
机构：
[1] Univ Monastir, Monastir, Tunisia
来源：
PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES | 2023年 / 37卷 / 03期
关键词：
Discrete-time martingales; Limit theorems; Reinforced processes; Stochastic approximation theory; Urn models; LIMIT-THEOREMS;
D O I：
10.1017/S0269964822000134
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we treat a nonlinear and unbalanced 2-color urn scheme, subjected to two different nonlinear drawing rules, depending on the color withdrawn. We prove a central limit theorem as well as a law of large numbers for the urn composition. We also give an estimate of the mean and variance of both types of balls.
引用
收藏
页码：711 / 729
页数：19
相关论文
共 25 条
  • [1] Aguech R., 2019, ARAB J MATH SCI, V26, P57
  • [2] [Anonymous], 2008, Polya urn models
  • [3] [Anonymous], 1923, Zeitschrift fur Angewandte Mathematik und Mechanik, DOI DOI 10.1002/ZAMM.19230030407
  • [4] ASYMPTOTIC NORMALITY IN THE GENERALIZED POLYA-EGGENBERGER URN MODEL, WITH AN APPLICATION TO COMPUTER-DATA STRUCTURES
    BAGCHI, A
    PAL, AK
    [J]. SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1985, 6 (03): : 394 - 405
  • [5] An adaptive design for multi-arm clinical trials
    Bai, ZD
    Hu, FF
    Shen, L
    [J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2002, 81 (01) : 1 - 18
  • [6] Asymptotic theorems for urn models with nonhomogeneous generating matrices
    Bai, ZD
    Hu, FF
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 80 (01) : 87 - 101
  • [7] Smoothing Equations for Large Plya Urns
    Chauvin, Brigitte
    Mailler, Cecile
    Pouyanne, Nicolas
    [J]. JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (03) : 923 - 957
  • [8] Chen MR, 2013, J APPL PROBAB, V50, P1169
  • [9] A new urn model
    Chen, MR
    Wei, CZ
    [J]. JOURNAL OF APPLIED PROBABILITY, 2005, 42 (04) : 964 - 976
  • [10] A SIMPLE URN MODEL
    FRIEDMAN, B
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1949, 2 (01) : 59 - 70
123