1. Definition
- let
be a renewal process
- Let
= reward earned at
-th renewal
- Assume
are i.i.d, but can depend on
(length of the
-th cycle)
Then
is a renewal reward process.
![Rendered by QuickLaTeX.com R(t) = sum^{N(t)}_{n=1} R_n](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-aa75685aec3effe9502234d57d0ce9cf_l3.png)
Intuitive explanation:
= cumulative reward earned up to time t
![Rendered by QuickLaTeX.com R(t)](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-b49df6234aae554fb49fed9d4d51be88_l3.png)
2. Renewal Reward Theorem
Proposition 7.3
Provided ![Rendered by QuickLaTeX.com E[R_n] < infty, E[X_n] < infty](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-716232bf33db1f64213028da321af8c2_l3.png)
![Rendered by QuickLaTeX.com E[R_n] < infty, E[X_n] < infty](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-716232bf33db1f64213028da321af8c2_l3.png)