  In this paper, we consider a non-Bayesian sequential change detection based
on the Cumulative Sum (CUSUM) algorithm employed by an energy harvesting sensor
where the distributions before and after the change are assumed to be known. In
a slotted discrete-time model, the sensor, exclusively powered by randomly
available harvested energy, obtains a sample and computes the log-likelihood
ratio of the two distributions if it has enough energy to sense and process a
sample. If it does not have enough energy in a given slot, it waits until it
harvests enough energy to perform the task in a future time slot. We derive
asymptotic expressions for the expected detection delay (when a change actually
occurs), and the asymptotic tail distribution of the run-length to a false
alarm (when a change never happens). We show that when the average harvested
energy ($\bar H$) is greater than or equal to the energy required to sense and
process a sample ($E_s$), standard existing asymptotic results for the CUSUM
test apply since the energy storage level at the sensor is greater than $E_s$
after a sufficiently long time. However, when the $\bar H < E_s$, the energy
storage level can be modelled by a positive Harris recurrent Markov chain with
a unique stationary distribution. Using asymptotic results from Markov random
walk theory and associated nonlinear Markov renewal theory, we establish
asymptotic expressions for the expected detection delay and asymptotic
exponentiality of the tail distribution of the run-length to a false alarm in
this non-trivial case. Numerical results are provided to support the
theoretical results.
