Stochastic signal is used to describe a non deterministic signal, i.e. a signal with some kind of uncertainity. A random signal is, by definition, a stochastic signal with whole uncertainty, i.e. with autocorrelation function with an impulse at the origin and power spectrum completely flat.

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Dear Rufaida Hussain, I agree with you its very much confusing and to differentiate between two. Both of processes are governed by probabilistic laws. But always I found in the books like "Stochastic or random signals: a signal whose value has some element of chance associated with it, therefore it cannot be predicted exactly".

For me, those concepts mean exactly the same.

I think they are not the same. In electrical engineering, we can build stochastic signal generator which supplies a signal with semi-random fashion (as I name it). This signal is not exactly random because we can model it in some equations. It always oscillates around certain origins.

Another example in geology, the motions of bodies (planets, moons, etc.) are stochastic not random.

However we use random numbers to generate security codes because we cannot predict them.

These two notions are broadly the same. To set the question on a proper basis, the characterization of a phenomenon as random or not is subjective. It depends on the relative "position" of the observer that characterizes it and on the knowledge available to her.

Dear Rufaida Hussain, I want to add more knowledge to this question. With my experience I have come across with terminologies of random variables, random processes and stochastic processes, random differential equations and stochastic differential equations, random dynamical systems and stochastic dynamical systems. But it is from best of my memory that I have never come across with the terminology 'stochastic variable'.

A stochastic process is a family of random variables { X(t)|t belongs T} defined on a given probability space, indexed by the time variable t, where t varies over an index set T.

Just as a random variable assigns a number to each outcome sin a sample space S, a stochastic process assigns a sample function x(t,s) to each outcome s.

stochastic processes are multiple realizations of a particular random variable

Random process and stochastic processes are in general the same thing with different nomenclature I think

Dear Afaq Ahmad,

The question is: What is the difference between a random signal and a stochastic signal?

These two terms are in general interchangeable. However, I have seen some

books where "random process" is used when the deterministic

variable used is time "t". If the variable is "space" as in pixels in images, I have

seen the usage of the term "stochastic process". For 4D processes that appear in

space-time array processing they are called "random fields" as in markov random fields (MRF).

Not only that stochastic/random processes always have to be function of time variable , it could be function of any number of variables --like in wireless communications we always come across multivariablestochastic processes i.e processes depending on time ,delay, space where space could again be subdivided into parameters as per the coordinate systems(x,y and z for cartesian/ r,theta and phi for spherical etc.) .

Dear All,

My observation is that we use random variable x(t) but we never came across with terminology of stochastic variable.

Dear Mr. Afaq

The meaning is that any stochastic process which are functions of multiple parameters.

It could be time , charge density, space etc. and you could assign different moments for the Random Varibles defining the Random Processes(at any particular epoch the function values for all the sample functions could be mapped to a RV) constitutes with respect to each one keeping other as constant.

Dear Subhas Roy, If you look since begining we all are of the view that there is no clear difference between both. What I found is "My observation is that we use random variable x(t) but we never came across with terminology of stochastic variable". That is the only demarkation.

You are right and we all know about. The question is "What is difference".

Stochastic signal is used to describe a non deterministic signal, i.e. a signal with some kind of uncertainity. A random signal is, by definition, a stochastic signal with whole uncertainty, i.e. with autocorrelation function with an impulse at the origin and power spectrum completely flat.

I've come across literatures -- Kleinrock on Queuing Theory & particularly from a literature on Stochastic processes by of Professor R Gallager and I quote it "Stochastic and random are synonyms, but random has become more popular for random variables and stochastic for stochastic processes. The reason for the author’s choice is that the common-sense intuition associated with randomness appears more important than mathematical precision in reasoning about rv’s,whereas for stochastic processes, common-sense intuition causes confusion much more frequently than with rv’s. The less familiar word stochastic warns the reader to be more careful"

So conclusion both are same.