Specifically, for each price vector $p$ in the finite set $P$, we define $\pi(p)$ as the time average fraction of time that $p(t) = p$, so that:
$$\lim_{t\to\infty}\frac{1}{t}\sum_{\tau=0}^{t-1}1\{p(\tau)=p\}=\pi(p) \quad\text{ with probability 1}$$ where $1\{p(\tau)-p\}$ is an indicator function that is $1$ if $p(\tau)=p$, and zero otherwise.
This excerpt was taken from "M. J. Neely. Stock market trading via stochastic network optimization. ArXiv Technical Report, arXiv:0909.3891v1, Sept. 2009."