  This paper focuses on estimating the invariant density function $f_X$ of the
strongly mixing stationary process $X_t$ in the multiplicative measurement
errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary
process. We propose a novel approach to handle non-independent data, typical in
real-world scenarios. For instance, data collected from various groups may
exhibit interdependencies within each group, resembling data generated from
$m$-dependent stationary processes, a subset of stationary processes. This
study extends the applicability of the model $Y_t = X_t U_t$ to diverse
scientific domains dealing with complex dependent data. The paper outlines our
estimation techniques, discusses convergence rates, establishes a lower bound
on the minimax risk, and demonstrates the asymptotic normality of the estimator
for $f_X$ under smooth error distributions. Through examples and simulations,
we showcase the efficacy of our estimator. The paper concludes by providing
proofs for the presented theoretical results.v
