  We perform a novel multi-messenger analysis for the identification and
parameter estimation of the Standing Accretion Shock Instability (SASI) in a
core collapse supernova with neutrino and gravitational wave (GW) signals. In
the neutrino channel, this method performs a likelihood ratio test for the
presence of SASI in the frequency domain. For gravitational wave signals we
process an event with a modified constrained likelihood method. Using simulated
supernova signals, the properties of the Hyper-Kamiokande neutrino detector,
and O3 LIGO Interferometric data, we produce the two-dimensional probability
density function (PDF) of the SASI activity indicator and calculate the
probability of detection $P_\mathrm{D}$ as well as the false identification
probability $P_\mathrm{FI}$. We discuss the probability to establish the
presence of the SASI as a function of the source distance in each observational
channel, as well as jointly. Compared to a single-messenger approach, the joint
analysis results in $P_\mathrm{D}$ (at $P_\mathrm{FI}=0.1$) of SASI activities
that is larger by up to $\approx~40\%$ for a distance to the supernova of 5
kpc. We also discuss how accurately the frequency and duration of the SASI
activity can be estimated in each channel separately. Our methodology is
suitable for implementation in a realistic data analysis and a multi-messenger
setting.
