Admistrivia
- Questions from the homework?
- Reading: chapter III up to and including section III.7.
Chapter III.6: Functionals of Random walks
Changing jump heights
- still easy as a martingale
How about the hitting time?
- Do p = q = .5 first.
- Write first step analysis
- Take diferences (I.e. let x = vk - vk-1)
- x's can be solved easilly
- Now solve for v's
-
Cash management (Time permitting)
Consider pawn shop: money in and money out.
alternatively, consider supply of 5 dollar bills: sometimes increase
sometimes decrease.
View as random walk. Want hitting time.
Chapter III.5.3: Success runs
Success runs processes
- "double or nothing"
- Failure goes back to beginning
- Called renewal process
Dean P. Foster
Last modified: Tue Oct 4 13:19:47 EDT 2011