

\subsection{\bf Markov Chains}

\begin{slide}
\begin{itemize}
\item One can generalize either the discrete or continuous time cases
by considering a system with again states $E_n$ and now not

\begin{description}
\item{$\bullet$} only transitions $E_n \rightarrow E_{n\pm 1}$ 
\item{$\bullet$} but a general probability $p_{jk}$ (discrete) or
$p_{jk} dt$ (continuous) of transitions from $E_j$ to $E_k$ at each
trial.
\end{description}

\item This theory includes general random walk problem and is discussed
in Volume 1, Feller.

\item The mathematics is not very deep---solving recurrence
relations---and the techniques are not useful for the basic problem in
physics (statistics of data reduction).

\item So I will not consider further.  People with biological bent
should, however, read further in Feller.

\item This Markov theory is relevant in discussions of the so called
Metropolis Method in Monte Carlo integration.
\end{itemize}
\end{slide}

