<< Chapter < Page
  Random processes   Page 1 / 1
Chapter >> Page >
This module introduces stationarity, such as strict sense stationarity (SSS) and wide sense stationarity (WSS).

Stationarity in a Random Process implies that its statistical characteristics do not change with time . Put another way, if one were to observe a stationary random process at some time t it would be impossible to distinguish the statistical characteristics at that time from those at some other time t .

Strict sense stationarity (sss)

Choose a Random Vector of length N from a Random Process:

X X t 1 X t 2 X t N
Its N th order cdf is
F X ( t 1 ) ,     X ( t N ) x 1 x N X t 1 x 1 X t N x N
X t is defined to be Strict Sense Stationary iff:
F X ( t 1 ) ,     X ( t N ) x 1 x N F X ( t 1 + c ) ,     X ( t N + c ) x 1 x N
for all time shifts c , all finite N and all sets of time points t 1 t N .

Wide sense (weak) stationarity (wss)

If we are only interested in the properties of moments up to 2nd order (mean, autocorrelation, covariance, ...), which isthe case for many practical applications, a weaker form of stationarity can be useful:

X t is defined to be Wide Sense Stationary (or Weakly Stationary) iff:

  • The mean value is independent of t , for all t
    X t μ
  • Autocorrelation depends only upon τ t 2 t 1 , for all t 1
    X t 1 X t 2 X t 1 X t 1 τ r X X τ
Note that, since 2nd-order moments are defined in terms of2nd-order probability distributions, strict sense stationary processes are always wide-sense stationary, but not necessarily vice versa .

Questions & Answers

a diagram of an adult mosquito
mubarak Reply
what are white blood cells
Mlungisi Reply
white blood cell is part of the immune system. that help fight the infection.
MG
what about tissue celss
Mlungisi
Cells with a similar function, form a tissue. For example the nervous tissue is composed by cells:neurons and glia cells. Muscle tissue, is composed by different cells.
Anastasiya
I need further explanation coz celewi anything guys,,,
Calvin Reply
hey guys
Isala
on what?
Anastasiya
is air homogenous or hetrogenous
damiane Reply
homogenous
Kevin
why saying homogenous?
Isala
explain if oxygen is necessary for photosynthesis
Allice Reply
explain if oxygen is necessary for photosynthesis
Allice Reply
Yes, the plant does need oxygen. The plant uses oxygen, water, light, and produced food. The plant use process called photosynthesis.
MG
By using the energy of sunlight, plants convert carbon dioxide and water into carbohydrates and oxygen by photosynthesis. This happens during the day and sunlight is needed.
NOBLE
no. it s a product of the process
Anastasiya
yet still is it needed?
NOBLE
no. The reaction is: 6CO2+6H20+ solar energy =C6H12O6(glucose)+602. The plant requires Carbon dioxyde, light, and water Only, and produces glucose and oxygen( which is a waste).
Anastasiya
what was the question
NOBLE Reply
joining
Godfrey
the specific one
NOBLE
the study of non and living organism is called.
Godfrey
Is call biology
Alohan
yeah
NOBLE
yes
Usher
what Is ecology
Musonda Reply
what is a cell
Emmanuel Reply
A cell is a basic structure and functional unit of life
Ndongya
what is biolgy
Hawwi Reply
is the study of living and non living organisms
Ahmed
may u draw the female organ
MARTIN Reply
i dont understand
Asal
:/
Asal
me too
DAVID
anabolism and catabolism
Sani Reply
Anabolism refers to the process in methabolism in which complex molecules are formed "built" and requires energy to happen. Catabolism is the opposite process: complex molecules are deconstructed releasing energy, such as during glicolysis.
Anastasiya
Explain briefly independent assortment gene .
Otu Reply
hi
Amargo
hi I'm Anatalia
Joy
what do you mean by pituitary gland
Digambar
draw and lable the cell
Ameh Reply
why homones are destroyed soon after completing their role
Nyirenda Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Random processes. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10204/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Random processes' conversation and receive update notifications?

Ask