0

Consider the Ehrenfest urn model with $N$ identical balls divided in two urns $A$ and $B$. At each step, pick a ball at random and switch its urn.

I need to compute $E_{N-1}(\tau_N) $ which is the expected hitting time for the state in which all the balls are in urn $A$ starting from a state in which $N-1$ balls are in urn $A$.

Can someone point me in the right direction ? I tried to solve it recursively but did not get to far.

Edit:I think I can use the expected return time from N to N and then minus one will get me what I want. The expected return time from N to N is $1/\pi(N)$ where $\pi$ is the stationary distribution. Is this idea in the right direction ?

Thanks!

Tomer
  • 434
  • Can you show details of what you tried? – Jose Avilez May 18 '22 at 00:04
  • I think I can use the expected return time from N to N and then minus one will get me what I want. The expected return time from N to N is $1/\pi(N)$ where $\pi$ is the stationary distribution. Is this idea in the right direction ? – Tomer May 18 '22 at 00:55

0 Answers0