Explicitly Constrained Stochastic Differential Equations on Manifolds

TL;DR

This paper develops methods for solving stochastic differential algebraic equations constrained on manifolds, enabling intrinsic modeling of stochastic processes with explicit algebraic constraints on geometric spaces.

Contribution

It introduces a framework for formulating and computing solutions of SDAEs on manifolds, extending existing stochastic differential equation techniques to constrained geometric settings.

Findings

Methods for solving SDAEs on manifolds are proposed.

The approach handles explicit algebraic constraints effectively.

Framework enables intrinsic stochastic modeling on geometric spaces.

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.