  This work investigates the problem of analyzing privacy for general Markov
processes. These processes may be affected by changes, or exogenous signals,
that need to remain private. Privacy refers to the disclosure of information of
these changes through observations of the underlying Markov chain. In contrast
to previous work on privacy, we study the problem for an online sequence of
data. We use theoretical tools from optimal detection theory to motivate a
definition of online privacy based on the average amount of information per
observation of the stochastic system in consideration. Two cases are
considered: the full-information case, where the eavesdropper measures all but
the signals that indicate a change, and the limited-information case, where the
eavesdropper only measures the state of the Markov process. For both cases, we
provide ways to derive privacy upper-bounds and compute policies that attain a
higher privacy level. It turns out that the problem of computing privacy-aware
policies is concave, and we conclude with some examples and numerical
simulations for both cases.
