工程随机过程_2_随机过程基本概念和分类.pdf

第二章 随机过程的 基本概念及分类 College of Science, Hohai UniversityCollege of Science, Hohai University Stochastic ProcessesStochastic Processes 引例 例1 用X (t)表示某手机在大年初一早上从8:00开 始经过t 时刻收到的短信数。 例2 顾客来到服务站要求服务，当服务站中的 服务员都正在为别的顾客服务时，来到的顾客 就要排队等待服务。由于顾客的来到时间一般 是随机的，每个顾客所需要的服务时间一般也 是随机的，令X (t)表示t 时刻的队长(服务的顾客 加等待的顾客) ，Y(t)表示为t 时刻来到的顾客所 需要等待的时间。 College of Science, Hohai University Stochastic Processes 例3 用X (t)表示南京下关某处t 日早上8:00的水 位高度。 例4 设质点Q在一直线上移动，每单位时间移动 一次，且只能在整数点上移动。用X (t)表示t 时 刻该质点所处的位置。 College of Science, Hohai University Stochastic Processes 例5 Vertical Density Profile (VDP) Manufacturers of engineered wood boards, which include particleboard and medium density fiberboard, are very concerned about the density properties of the board because they determine its machinability. The density is measured using a profilometer that uses a laser device to take measurements at fixed depths across the thickness of the board. The measurements on a sample form the vertical density profile(VDP) of the board. This VDP consists of 314 measurements taken 0.002 inches apart. 24 profiles are shown in Figure. College of Science, Hohai University Stochastic Processes 24 profiles in Vertical Density Profile (VDP) College of Science, Hohai University Stochastic Processes 随机过程的定义 (, F, P)为一概率空间，T(, +)为参数 集。若对任一t T，有一个定义在(, F, P)随机 变量X (t, )(或X ()), , 与之对应, 则称{X (t, t ), t T}为随机过程(Stochastic Processes) 。简记 {X (t), t T}(或{X , t T})(s.p.) 。 t 随机过程的值域E(状态空间) ： 随机过程{X (t), t T }的可能取值范围。 随机过程的状态：E 中的元素。 College of Science, Hohai University