# Thread: Erhenfest process

1. ## Erhenfest process

thank you so much

2. ## Re: Erhenfest process

Hey pupupanda.

Have you solved for the standard pi terms using the normal Markov method?

3. ## Re: Erhenfest process

I have no idea where to start

4. ## Re: Erhenfest process

There is a technique to solve for stationary states.

Do you know what a stationary state is in a Markov process/chain?

5. ## Re: Erhenfest process

Originally Posted by chiro
There is a technique to solve for stationary states.

Do you know what a stationary state is in a Markov process/chain?
Yes. I know what a stationary state is. How is this relate to the question?
Thanks

從我的iPhone使用Tapatalk 發送

6. ## Re: Erhenfest process

These are stationary states if the terminology you are using is correct.

7. ## Re: Erhenfest process

Originally Posted by chiro
These are stationary states if the terminology you are using is correct.
I don't know how to prove it. Stationary distribution is a stochastic process {Xt: t>_0} is stationary if for any k>_ 0 and any m>_t, the joint distribution of (Xt,....Xm) is the same as the joint distribution of (Xt+k,...Xm+k), right?
I don't know how to apply it to this problem

從我的iPhone使用Tapatalk 發送

8. ## Re: Erhenfest process

Stationary states can be derived with an expression for the values of the matrix.

The idea is that pi_(j) = Sum [i=0 to M] pi(i) * p(i,j) where pi(x) is the stationary probability for state x and p(i,j) is the probability value in the Markov chain matrix.

They are also probabilities meaning they are between 0 and 1 inclusive and all add up to unity.

9. ## Re: Erhenfest process

Originally Posted by chiro
Stationary states can be derived with an expression for the values of the matrix.

The idea is that pi_(j) = Sum [i=0 to M] pi(i) * p(i,j) where pi(x) is the stationary probability for state x and p(i,j) is the probability value in the Markov chain matrix.

They are also probabilities meaning they are between 0 and 1 inclusive and all add up to unity.
I don't know how to work out the transition matrix for this case

從我的iPhone使用Tapatalk 發送

10. ## Re: Erhenfest process

can you help me to guidance where should I start this? then I can to continue.

11. ## Re: Erhenfest process

Can you state information about the process? Anything on your notes regarding transition probabilities for this process?

12. ## Re: Erhenfest process

Originally Posted by chiro
Can you state information about the process? Anything on your notes regarding transition probabilities for this process?
I already solve the problem with the stationary distribution. Thanks

從我的iPhone使用Tapatalk 發送