The Friedman's urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been ...The Friedman's urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman's urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.展开更多
This paper attempts to trace the influence of Jorge Luis Borges on Ge Fei. It shows that Ge Fei＇s stories share Borges＇s narrative form though they do not have the same philosophical premises as Borges＇s to support...This paper attempts to trace the influence of Jorge Luis Borges on Ge Fei. It shows that Ge Fei＇s stories share Borges＇s narrative form though they do not have the same philosophical premises as Borges＇s to support them. What underlies Borges＇s narrative complexity is his notion of the inaccessibility of reality or divinity and his understanding of the human intellectual history as epistemological metaphors. While Borges＇s creation of narrative gap coincides with his intention of demonstrating the impossibility of the pursuit of knowledge and order, Ge Fei borrows this narrative technique from Borges to facilitate the inclusion of multiple motives and subject matters in one single story, which denotes various possible directions in which history, as well as story, may go. Borges prefers the Jungian concept of archetypal human actions and deeds, whereas Ge Fei tends to use the Freudian psychoanalysis to explore the laws governing human behaviors. But there is a perceivable connection between Ge Fei＇s rejection of linear history and traditional storyline with Borges＇ explication of epistemological uncertainty, hence the former＇s tremendous debt to the latter. Both writers have found the conventional narrative mode, which emphasizes the telling of a coherent story having a beginning, a middle, and an end, inadequate to convey their respective ideational intents.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071214)Natural Science Foundation of Zhejiang Province (Grant No. R6100119)+1 种基金the Program for New Century Excellent Talents in University (Grant No. NCET-08-0481)Department of Education of Zhejiang Province(Grant No. 20070219)
文摘The Friedman's urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman's urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.
文摘This paper attempts to trace the influence of Jorge Luis Borges on Ge Fei. It shows that Ge Fei＇s stories share Borges＇s narrative form though they do not have the same philosophical premises as Borges＇s to support them. What underlies Borges＇s narrative complexity is his notion of the inaccessibility of reality or divinity and his understanding of the human intellectual history as epistemological metaphors. While Borges＇s creation of narrative gap coincides with his intention of demonstrating the impossibility of the pursuit of knowledge and order, Ge Fei borrows this narrative technique from Borges to facilitate the inclusion of multiple motives and subject matters in one single story, which denotes various possible directions in which history, as well as story, may go. Borges prefers the Jungian concept of archetypal human actions and deeds, whereas Ge Fei tends to use the Freudian psychoanalysis to explore the laws governing human behaviors. But there is a perceivable connection between Ge Fei＇s rejection of linear history and traditional storyline with Borges＇ explication of epistemological uncertainty, hence the former＇s tremendous debt to the latter. Both writers have found the conventional narrative mode, which emphasizes the telling of a coherent story having a beginning, a middle, and an end, inadequate to convey their respective ideational intents.
