Случайные процессы и динамические системы. Термины и определения

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Random processes and dynamical Systems.
Terms and definitions

ei=xi,-.,; n =x n ),
3. 4. ;(^ ■?■?■?•^Un) < * ( dx v ..dx n

5. Characteristical function
6. / (0= =JxdF < (x), V (G / = 7 ••• H(x 1 ,...,x n )dF t t
_oo _cc tl '--,*.n
Pt„^,...,t n ^’ x "-’- ’ Mf= s ••• X 8. Random process variance
(/)=2

9. Standard deviation of a random process =]/ ” 2 ””’ '-

13. 4,- (1=1, 2,..., =W( ^ = - '‘ ■? ■?■?

Correlation coefficient 19. 20. s 7 £?# s
? f S S m 1 7
~ — -— .

21. First-order random process
Continuous random process Random sequences Discrete random sequences
27. Determinate process Periodic process
29. Nonperiodic process + $(/) : Quasi-determinate process
3rl. Mutually independant random processes t(t) : 1=1
F < Xn ) X
X F , . ()'i,...,y m )
1 n ’

3-3. 34. White noise 35. 36. ?(0 =
/?( R(t,x)^Q
1. 1) =
= Wt n ,t n _y x n. '-^ = 1 tl< ...< t n ,

Gaussian process
38. Random process with stationary in a narrow sense increments
39. Random process with stationary in a wide sense increments
40. Random process with orthogonal increments 2. =(2r.) Xl-v/— mj], ‘I Vf/ fe=l
...... t n ^ tl ~ x ue - ’ Xt n~ X “n^
...,X( j-_— x a 4-^) n n
( M(lx t -x u i 2 ) = M(Jx t+ , -
i(i): At[ ( Additive process
42. Poisson process
43. Wiener process [/■?(<- u)] fe - 1 — ■? : =- 1 2 Random process with uncorrelated increments
45. MfO,., — -x a , )M(a,, — x IH )
/)--:( t) -rn. ( /)

46. =F t 1 +- t + -,y m )^ F t 1+z

49. Stationary dependent in Narrow-band stationary random process
51. Wide-band stationary random process
52. Random stationary process with boundet spectrum 53. Ergodic process
;( 0. 7 i( 0 ! S(to)a0 ;(<) *V*67’,P[<f>=W] = l, <7> = < =lim si- HRUi+0.-
Z-*oo 27 -T

54. =lim ■?••.’ 55. Power spectral density function
57. Cross-power spectral density function of stationary dependent random processes
59. First-order system
64. Multivariable system Linear system (t), 66. Nonlinear system — ¥?= S ■? 70. 71. Lumped parameter system
72. Long line Is

= ( ( Unit pulse response 1, ( Trasfer function H(s)^ Wnc dt, 0
( a?-
0
, = , A (. ''>) Gain-frequency characteristic Phase-frequency characteristic ■?Real frequency response Rc Imaginary frequency response
82.

(55) 8
(3) (4) (6)
(56)55
(17) (20) (72)
6 7
7
(12)
( (13)
( (10) ( 9
4
4
(56)
5-8 56
24 26
(27) (33) (46)
(1) 43
(36) 37 27 30
36 29
(27' 28 32 42
(27) (25) (47)

Additive process 41
Autocorrelation function 16-
Autocovariation function Characteristical function 5
Continuous random process 23
Correlation coefficient 17
Correlation noise 35
Cross—correlation function 19
Cross—covariation function 18
Cross spectral density function of stationary dependent random processes 58
Determinate process 27
Determinate system 64
Discrete random sequences 26
Dxnamical system 2
Ergodic process 53
First—order random process 22
First—order system 62
Gain—frecuency characteristic 78
Gaussian process 37
Generalized frecuency function 77
Imaginary frecuency response 81
Joint v— tli order n+m dimensional distribution moment for two random processes '14
Linear system 65
Long line 72
Lumped parameter system 71
Marcovian process 36-
Mathematical expectation of a random process 6
Multivariable system 64
Mutually ergodic processes 54
Mutually independent random processes 31
n-dimensional mathematical expectation of a random process function 7
n-dimensional probability density function 4
n-dimensional probability distribution function 3
n-dimensional random process 22
n-order random process 32
Narrow-band stationary random process 50
Nonanticipativs dynamical system 59
Nonlinear system 66
Nonperiodic process 29
Nonstationary system 70'
Periodic process 28
Phase-frecuecy characteristic 79
Poisson process 42
Power spectral density function 56
Quasi-determinate process 30
Random process 1
Random process variance &
Random process with orthogonal increments 40
Random process with stationary in a narrow sense increments 38
Random process with stationary in a wide sense increments 39
Random process with uncorrelated increments 44
Random sequences 24
Random stationary process with boundet spectrum 52’
Random system 62
Real frecuency response 80
Standard deviation of a random process &
Stationary dependent in a narrow sense random process 48
Stationary dependent in a wide sense random process 49
Stationary in a narrow sense random process 46
Stationary in a wide sense random process 47
Stationary system 69
Trasfer function 76
Unit pulse response 75
Weight function 74
White nois in a narrow sense 33
White noise in a wide sense 34
Wide-band stationary random process 51
Wiener process 43
v-th order n-dimensional distribution absolute central moment 13
v-th order n-dimensional distribution absolute moment 12
v-th order n-dimensional distribution central moment 11
v-th order n-dimensional distribution moment 10
Random variable
2. 3. Probability density function of a random variable dF(x)

Characteristical junction Main value of Variable of random variable 7. 8. Standart deriation 9. V - -

Distribution function of ’1 < < dx=(dx 1 ,dx 2 ,.-. i dx n )