Stochastic differential equations on Banach manifolds (Q2711777)

The theory of stochastic differential equations on infinite dimensional manifolds was developed by \textit{Ya. I. Belopolskaya} and \textit{Yu. L. Daletskii} [Trans. Mosc. Math. Soc. 1, 113-150 (1980; Zbl 0439.60052)] for Itô's equations on Hilbert manifolds or Banach manifolds modelled on Banach spaces with smooth norms. NEWLINENEWLINENEWLINEThe authors consider the Stratonovich type equations on Banach manifolds modelled on more general M-type 2 Banach spaces. It is shown that some Sobolev-Slobodetskii spaces belong to this class and the Nemytski maps are locally Lipschitz on them. Besov-Slobodetskii spaces of loops on Riemannian manifolds are constructed, with their manifold structure, of such a class that the natural Brownian motion induced measures of stochastic analysis are supported on them. Some special stochastic differential equations are constructed on these loop spaces. Non explosion conditions are given.