Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have looked around the literature but I've not found a clean answer to the following. Imagine that you have a generalized PĆ³lya urn (GPU) in the sense of Pemantle's survey (Section 2.1 in Pemantle07). What is the expected time until the ratio of white balls to black balls is equal to $p$ (assuming that the initial ratio is $p_0$)? An answer for the much simpler case of the GPU with a diagonal $A$ matrix would also be interesting. A non-trivial upper bound would also suffice.

share|cite|improve this question
    
There is more than one way to generalise a Pólya urn, so you may need to give more detail. In many cases I would think the answer to your question will be an infinite expectation or worse. – Henry Sep 11 '11 at 17:00

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.