Explicitly Constrained Stochastic Differential Equations on Manifolds

Abstract

In this manuscript we consider Intrinsic Stochastic Differential Equations on manifolds and constrain it to a level set of a smooth function. Such type of constraints are known as explicit algebraic constraints. The system of differential equation and the algebraic constraints is, in combination, called the Stochastic Differential Algebraic Equations (SDAEs). We consider these equations on manifolds and present methods for computing the solution of SDAEs on manifolds.

Typos have been corrected in this version e.g., in the previous version an additional term wrongly added in the solution of proposition 4.1 due to a typographic error in writing the generalized Ito formula