A practical global existence and uniqueness result for stochastic differential equations on Riemannian manifolds of bounded geometry

Matthias Rakotomalala (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this paper, we establish a result for existence and uniqueness of stochastic differential equa- tions on Riemannian manifolds, for regular inhomogeneous tensor coefficients with stochastic drift, under geometrical-only hypothesis on the manifold, so-called manifolds of bounded geometry, this hypothesis is consistent with the maximal regularity result for parabolic equations obtained by Herbert Amann. Furthermore, we provide a stochastic flow estimate for the solutions.

Keywords: Stochastic differential equation; Riemaniann Manifold

Domains: Probability [math.PR]

Matthias Rakotomalala. A practical global existence and uniqueness result for stochastic differential equations on Riemannian manifolds of bounded geometry. 2024. ⟨hal-04548350v2⟩