Globalizations of infinitesimal actions on supermanifolds

Let $\mathcal{G}$ be a Lie supergroup with Lie superalgebra $\mathfrak{g}$, $\mathcal{M}$ a supermanifold and $\mathrm{V}\mathrm{e}\mathrm{c}(\mathcal{M})$ the set of vector fields on $\mathcal{M}$. Let $\lambda:\mathfrak g\rightarrow $\mathrm{V}\mathrm{e}\mathrm{c}$(\mathcal M)$ be an infinitesimal action, i.e. a homomorphism of Lie superalgebras. We show the existence of a local $\mathcal{G}$-action on $\mathcal{M}$ inducing the infinitesimal action $\lambda$ and find necessary and sufficient conditions for the existence of a globalization in the sense of Palais.