منابع مشابه
A New Urn Model
In this paper, we propose a new urn model. A single urn contains b black balls and w white balls. For each observation, we randomly drawm balls and note their colors, say k black balls andm−k white balls. We return the drawn balls to the urn with an additional ck black balls and c(m− k) white balls. We repeat this procedure n times and denote by Xn the fraction of black balls after the nth draw...
متن کاملA note on randomized Shepp's urn scheme
Shepp’s urn model is a useful tool for analyzing the stopping-rule problems in economics and finance. In [R.W. Chen, A. Zame, C.T. Lin, H. Wu, A random version of Shepp’s urn scheme, SIAM J. Discrete Math. 19 (1) (2005) 149–164], Chen et al. considered a random version of Shepp’s urn scheme and showed that a simple drawing policy (called “the k in the hole policy”) can asymptotically maximize t...
متن کاملAsymptotics in Randomized Urn Models
This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2, . . . , n− 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition a...
متن کاملNonlinear Ehrenfest's urn model.
Ehrenfest's urn model is modified by introducing nonlinear terms in the associated transition probabilities. It is shown that these modifications lead, in the continuous limit, to a Fokker-Planck equation characterized by two competing diffusion terms, namely, the usual linear one and a nonlinear diffusion term typical of anomalous diffusion. By considering a generalized H theorem, the associat...
متن کاملRandomized Urn Models revisited using Stochastic Approximation
This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in [5, 6, 7]. We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (Central Limit Theorem CLT ) of the no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2012
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2012.312a292