随机过程英语讲义-1

句号，点 竖线
vertical bar, vertical virgule
& * / // # \ ~
amp;
ampersand, and, reference, ref
和，引用
asterisk, multiply, star, pointer
星号，乘号，星，指针
slash, divide, oblique 斜线，斜杠，除号 slash-slash, comment 双斜线，注释符 pound 井号
backslash, sometimes escape 反斜线转义符，有时表 示转义符或续行符 tilde 波浪符
'
apostrophe hyphen
撇号[ə'pɔstrəfi]
-...
‘’
连字号
dash 破折号 dots/ ellipsis 省略号 single quotation marks 单引号 double quotation marks 双引号 parallel 双线号 arrow 箭号；参见号
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网络诱导的问题
执行器 执行器 控制对象 传感器 传感器
y(k) y(k)
控制对象
网
络
网
络
y(k)
数据丢失 数据丢失 y(k) 延时 乱序
…
控制器 控制器
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执行器
控制对象 传感器
y(k)
延 时
网
络 y(k-1)
控制器
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延 时
执行器
控制对象 传感器
y(k+1)
网
络 y(k-1)
y(k)
控制器
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We shall suppose that for each event E of the sample space S a number P(E) is defined and satisfies the following three axioms: Axiom (1) 0 ≤ P(E) ≤ 1. Axiom (2) P(S)=1. Axiom (3) For any sequence of events E1 , E2 ,…that are mutually exclusive, that is, events for which Ei∩Ej=Φ when i≠ j (where Φ is the null set) ,
(square) root ∵ ∴ ∪ ∩ ∫ ∑
since; because hence 所以
union of 并，合集 intersection of 交，通集 the integral of …的积分 (sigma) summation of 总和
{ } ( ) () [ ] [] . |
open brace, open curly close brace, close curly
大写 Capital, A “Capital A”
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CHAPTER 1 Preliminaries
1.1 Probability
A basic notion in probability theory is random experiment : an experiment whose outcome cannot be determined in advance. The set of all possible outcomes of an experiment is called the sample space of that experiment , and we denote it by S.
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About Reference Book
本书是国际知名统计学家Sheldon M．Ross所著的关于 基础概率理论和随机过程的经典教材，被加州大学伯克利分 校、哥伦比亚大学、普度大学、密歇根大学、俄勒冈州立大 学、华盛顿大学等众多国外知名大学所采用。
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一些特殊数学符号的英语读法
+ plus minus 加号；正号 减号；负号 正负号 乘号
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执行器
控制对象
传感器
y(k+2)
乱 序
网
络 y(k-1)
y(k+1)
控制器
y(k)
Solution: Denote sample space by S then, S = { 1, 2, 3, …, }.
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Problem 2: Measure the time between two message arrivals at a message center. Solution: Denote sample space by S then, S = { t: t ≥ 0 } = [ 0, where t denotes time. ),
STOCHASTIC PROCESSES AND ITS APPLICATIONS
Prof. Xia Yuanqing
School of Automation Beijing Institute of Technology E-mail:yuanqing.xia@gmail.com
Assistant
P (U Ei ) = ∑ P( Ei )
i =1 i =1
∞
∞
We refer to P(E) as the probability of the event E.
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Some simple consequences of axioms (1) , (2) , and (3) are :
The inequality (1.1.4) is known as Boole’s inequality.
“” ‖ →
上标（superscript) 下标（subscript) 读法应为 w subscript 0 也可以这样 w sub 0 读法应为 f superscript t 也可以这样 f sup t 其他一些数学上的读法 a to the nth power or a to the nth Ai,j A* A‘ pronouced as "A i comma j" pronouced as "A star" or " A asterisk" “A prime ” or “A apostrophe
左花括号 右花括号
open parenthesis [pə‘renθəsis], open paren 左圆括号 close parenthesis, close paren brakets/ parentheses open bracket 左方括号 close bracket 右方括号 square brackets period, dot 方括号 括号 右圆括号
The probability of the outcome k :
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An important property of the probability function P is that it is continuous . To make this more precise, we need the concept of a limiting event .
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The relative frequency of an outcome k： For n trials,
Statistical regularity: Averages obtained in long sequences of trials of random experiments consistently yield approximately the same value.
Sheldon M. Ross Epstein Chair Professor Industrial and Systems Engineering Phone: (213) 740-4893 Email: smross@usc.edu
Education Dr. Ross received his B. S. degree in Mathematics from Brooklyn College in 1963. He received his M.S. degrees in Mathematics from Purdue University in 1964 and his Ph.D. degree in Statistics from Stanford University in 1968.
If {En , n ≥ 1} is an increasing sequence of events , then we define a new event , denoted by lim En by
n →∞
lim En = U Ei , when En ⊂ En +1 , n ≥ 1 .
n →∞ i =1
We define as follows : A sequence of events {En , n ≥ 1} is said to be an increasing sequence if En ⊂ En +1 , n ≥ 1 and is said to be decreasing if En ⊃ En +1 , n ≥ 1 .
Problem 1: A block is transmitted repeatedly over a noisy channel until an error-free block arrives at the receiver. Count the number of transmission required. For example, in networked control systems
Sheldon M. Ross Professor Ph.D. Stanford University, 1968 statistics E-mail: ross ieor.berkeley.edu
Research： Stochastic Models Simulation Statistical Analysis Financial Engineering
Dai Li
School of Automation Beijing Institute of Technology E-mail:daili1887@gmail.com
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About Reference Book
STOCHASTIC PROCESSES
Second Edition
Sheldon M.Ross
± plus or minus × is multiplied by ÷ is divided by ≠ is not equal to = is equal to
除号 不等于号
等于号 全等于号
≡ is equivalent to
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< > ≤ ≥ ∞ ∝
is less than 小于号 is more than 大于号 is less than or equal to 小于或等于号 is more than or equal to 大于或等于号 infinity 无限大号 varies as 与…成比例 平方根 因为
∞
Similarly if {En , n ≥ 1} is an decreasing sequence , then define lim En
An event is a subset of a sample space , and is said to occur if the outcome of the experiment is an element of that subset.
Problem : Write the values of events for problems in case study of sample space for following events: 1、Fewer than 10 transmission are required 2、Less than t0 seconds elapse between message arrivals Solution :1、Fewer than 10 transmission are required A = { 1, 2, … , 9 } 2、 Less than t0 seconds elapse between message arrivals A = { t : 0 ≤ t < t0 }= [ wenku.baidu.com, t0 )