We discuss a method that analyzes time series generated by point processes to detect possible non stationarity in
the data. We interpret each observation as the first passage time of a stochastic process through a deterministic
boundary and we concentrate the effect of different dynamics on the boundary shape. We propose an estimator
for the boundary and we compute its confidence intervals. Applying the Inverse First Passage Time Algorithm
we then recognize the evolution in the dynamics of the time series by means of a comparison of the boundary
shapes. This is performed using a suitable time window fragmentation on the observed data.
KEYWORDS: Signal detection, Interference (communication), Signal processing, Reliability, Stochastic processes, Diffusion, Measurement devices, Telecommunications, Systems modeling, Process modeling
Noise is generally considered a disturbance in understanding systems dynamics and large efforts are devoted
to filter its presence in observed data. In many instances the filtering helps the comprehension of involved
phenomena but this cleaning can result in a distruction of important information. A set of examples, extracted
from existing mathematical and applied literature, illustrate instances where the noise plays a positive role in
determining the final dynamics of the system or allowing optimum values for signal detection. In this paper
we will specifically focus on possible roles of noise when the underlining system presents non-linearities. Some
of the discussed examples are toy examples useful to explain some unexpected result but we also consider the
mathematical problem of determining the first passage times of stochastic processes through boundaries. These
times have an immediate role in reliability theory, when alarms are tuned to prevent crashes. The fact that their
behavior is highly determined by a positive role of the noise can suggest improvements for some measurement
device.
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