MHB Need help with probability question. probability of dependent events.

[Mewlove]

Would like to know what method, or distribution to use when solving a problem like this:I start from level 0. There is a probability p chance to drop to level -1 and a (1-p) chance to increase to level 1.

The levels range from level -n to level n. When it reaches level -n or level n, it resets back to 0 on the same cycle.
(Also, if you are at level -1, there is (1-p) chance to go back to level 0)

How do I calculate the percentage of landing on each level (not counting the reset), assuming I continue running this infinitely? Seems like dependent events. Is there any theorem or formula I can use?

Thanks!

 

[StoneTemplePython]

what you're looking for here is a finite state (recurrent, time homogenous) markov chain. Depending on whether your n is even or odd, the chain may actually be periodic with period 2 but that is a minor complication-- you want to solve for the eigenvector that gives a steady state probability distribution.

the key thing to search for is 'finite state markov chain'