  The switch process alternates independently between 1 and -1, with the first
switch to 1 occurring at the origin. The expected value function of this
process is defined uniquely by the distribution of switching times. The
relation between the two is implicitly described through the Laplace transform,
which is difficult to use for determining if a given function is the expected
value function of some switch process. We derive an explicit relation under the
assumption of monotonicity of the expected value function. It is shown that
geometric divisible switching time distributions correspond to a non-negative
decreasing expected value function. Moreover, an explicit relation between the
switching time distribution and the autocovariance function of the switch
process stationary counterpart is obtained, which allows parallel results for
the stationary switch process and its covariance function. These results are
applicable to approximation methods in statistical physics, and an example is
presented.
