  The nuclear radio emission of low-luminosity active galactic nuclei (LLAGN)
is often associated with unresolved cores. In this paper we show that most
LLAGN present extended jet radio emission when observed with sufficient angular
resolution and sensitivity. They are thus able to power, at least, parsec-scale
radio jets. To increase the detection rate of jets in LLAGN, we analyze
subarcsecond resolution data of three low-ionization nuclear emission regions.
This yields the detection of extended jet-like radio structures in NGC\,1097
and NGC\,2911 and the first resolved parsec-scale jet of NGC\,4594 (Sombrero).
The three sources belong to a sample of nearby LLAGN for which
high-spatial-resolution spectral energy distribution of their core emission is
available. This allows us to study their accretion rate and jet power
($Q_\mathrm{jet}$) without drawing on (most) of the ad hoc assumptions usually
considered in large statistical surveys. We find that those LLAGN with
large-scale radio jets ($>$100 pc) have $Q_\mathrm{jet} > 10^{42}$ erg
s$^{-1}$, while the lowest $Q_\mathrm{jet}$ correspond to those LLAGN with
parsec-scale ($\leq$100 pc) jets. The $Q_\mathrm{jet}$ is at least as large as
the radiated bolometric luminosity for all LLAGN, in agreement with previous
statistical studies. Our detection of parsec-scale jets in individual objects
further shows that the kinematic jet contribution is equally important in
large- or parsec-scale objects. We also find that the Eddington-scaled
accretion rate is still highly sub-Eddington ($<10^{-4}$) when adding the
$Q_\mathrm{jet}$ to the total emitted luminosity (radiated plus kinetic). This
indicates that LLAGN are not only inefficient radiators but that they also
accrete inefficiently or are very efficient advectors.
