Mục đích chính của bài báo này là để thể hiện một xác suất số liệu dựa vào nhà điều hành nổi tiếng của Trotter. Một số ước tính liên quan đến tỷ lệ hội tụ thông qua Trotter số liệu được thành lập. | Vietnam Journal of Mathematics 35 1 2007 21-32 Viet n a m J 0 u r n a I of MATHEMATICS VAST 2007 On a Probability Metric Based on Trotter Operator Tran Loc Hung Hue College of Science Hue University 77 Nguyen Hue Hue Vietnam Received December 19 2005 Revised June 25 2006 Abstract. The main purpose of this paper is to present a probability metric based on well-known Trotter s operator. Some estimations related to the rates of convergence via Trotter metric are established. 2000 Mathematics Subject Classification 60G50 60E10 25 32U 05. Keywords Probability metric Trotter operator rates of convergence weak law of large numbers quicksort algorithm. 1. Introduction During the last several decades the probability metric approach has risen to become one of the most important tools available for dealing with certain types of large scale problems. In the solution of a number of problems of probability theory the method of distance function has attracted much attention and it has successfully been used lately as Abramov 1 Butzer and Kirschfink 4 Dudley 6 and 7 Kirschfink 12 Rachev 20 and Zolotarev 26-31 . The essence of this method is based on the knowledge of the properties of metrics in spaces of random variables as well as on the principle according to which in every problem of the approximating type a metric as a comparison measure must be selected in accordance with the requirements to its properties. In recent years several results of applied mathematics and informatics have been established by using the probability metric approach. Results of this nature may be found in Gibbs and Edward 9 Hutchinson and Ludger 11 and Ralph 22 Tran Loc Hung and Ludger 16 - 18 Hwang and Neininger 10 Mahmound and Neininger 13 . The main purpose of the present note is to introduce a probability metric which is based on well-known Trotter s operator. Some approximations of the rates of convergence via Trotter metric are indicated. This paper is organized as follows. Sec. 2 deals with some
