  A theory is formulated for time dependent fluctuations of the spectrum of a
single molecule in a dynamic environment. In particular, we investigate the
photon counting statistics of a single molecule undergoing a spectral diffusion
process. Based on the stochastic optical Bloch equation, fluctuations are
characterized by Mandel's $Q$ parameter yielding the variance of number of
emitted photons and the second order intensity correlation function,
$g^{(2)}(t)$. Using a semi-classical approach and linear response theory, we
show that the $Q$ parameter can be described by a three-time dipole correlation
function. This approach gene ralizes the Wiener-Khintchine formula that gives
the average number of fluorescent photons in terms of a one-time dipole
correlation function. We classify the time ordering properties of the
three-time dipole correlation function, and show that it can be represented by
three different pulse shape functions similar to those used in the context of
nonlinear spectroscopy. An exact solution is found for a single molecule whose
absorption frequency undergoes a two state random telegraph process (i.e., the
Kubo-Anderson sudden jump process.) Simple expressions are obtained from the
exact solution in the slow and fast modulation regimes based on appropriate
approximations for each case. In the slow modulation regime $Q$ can be large
even in the long time limit, while in the fast modulation regime it becomes
small.
