  We consider a class of single-particle one-dimensional stochastic equations
which include external field, additive and multiplicative noises. We use a
parameter $\theta \in [0,1]$ which enables the unification of the traditional
It\^o and Stratonovich approaches, now recovered respectively as the $\theta=0$
and $\theta=1/2$ particular cases to derive the associated Fokker-Planck
equation (FPE). These FPE is a {\it linear} one, and its stationary state is
given by a $q$-Gaussian distribution with $q = \frac{\tau + 2M (2 -
\theta)}{\tau + 2M (1 - \theta)}<3$, where $\tau \ge 0$ characterizes the
strength of the confining external field, and $M \ge 0$ is the (normalized)
amplitude of the multiplicative noise. We also calculate the standard kurtosis
$\kappa_1$ and the $q$-generalized kurtosis $\kappa_q$ (i.e., the standard
kurtosis but using the escort distribution instead of the direct one). Through
these two quantities we numerically follow the time evolution of the
distributions. Finally, we exhibit how these quantities can be used as
convenient calibrations for determining the index $q$ from numerical data
obtained through experiments, observations or numerical computations.
