  The aim of this study is to extend the scope and applicability of the
level-crossing method to discrete-time stochastic processes and generalize it
to enable us to study multiple discrete-time stochastic processes. In previous
versions of the level-crossing method, problems with it correspond to the fact
that this method had been developed for analyzing a continuous-time process or
at most a multiple continuous-time process in an individual manner. However,
since all empirical processes are discrete in time, the already-established
level-crossing method may not prove adequate for studying empirical processes.
Beyond this, due to the fact that most empirical processes are coupled; their
individual study could lead to vague results. To achieve the objectives of this
study, we first find an analytical expression for the average frequency of
crossing a level in a discrete-time process, giving the measure of the time
experienced for two consecutive crossings named as the "waiting time". We then
introduce the generalized level-crossing method by which the consideration of
coupling between the components of a multiple process becomes possible.
Finally, we provide an analytic solution when the components of a multiple
stochastic process are independent Gaussian white noises. The comparison of the
results obtained for coupled and uncoupled processes measures the strength and
efficiency of the coupling, justifying our model and analysis. The advantage of
the proposed method is its sensitivity to the slightest coupling and shortest
correlation length.
