  Any vertex algebra has a canonical decreasing filtration, called Li
filtration, whose associated graded space has a natural structure of a vertex
Poisson algebra. In this note, we introduce an analogous filtration for any
SUSY vertex algebra, which was introduced by Heluani and Kac as a superfield
formalism of a supersymmetric vertex algebra. We prove that the associated
graded superspace of our filtration has a structure of SUSY vertex Poisson
algebras. We also introduce and discuss related notions, such as Zhu's
$C_2$-Poisson superalgebras, associated superschemes and singular supports, for
SUSY vertex algebras.
