Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Independent Processes vs. Independent Random Variables
Replies: 1   Last Post: Dec 31, 2013 8:19 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Roland Franzius

Posts: 370
Registered: 12/7/04
Re: Independent Processes vs. Independent Random Variables
Posted: Dec 31, 2013 8:19 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Am 31.12.2013 12:50, schrieb bahram.ehsandoust@gmail.com:
> Hi all,
> I just noticed that for two stochastic processes, being independent

at each time instant doesn't mean that they are two independent processes.
> So, how can I check whether they are independent processes or not?
What is the technical definition of two independent stochastic processes?

All joint probabilities factorize

Pr[ And_k,l ( X_(t_k) \in dx_ k, Y_(t_l) \in dy_l ) ] =

Pr[ And_k ( X_(t_k) \in dx_ k) ] * Pr[And_l( Y_(t_l) \in dy_l )]

=rho(x_1,..x_n) dx^1 /\ ... dx^n /\

sigma(y_1,..y_m) dy^1 /\ ... dy^m

For processes with exponential, especially gaussian distributions with
factorizing transition probabilities its often enough to show that all
two point correlation functions are products anologously to showing the
independence of gaussian variables by checking the first two moments.


Roland Franzius

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.