Strong convergence of a half-explicit Euler scheme for constrained stochastic mechanical systems

Abstract

This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. The considered systems are described by second-order stochastic differential-algebraic equations involving an implicitly given Lagrange multiplier process. The explicit representation of the Lagrange multiplier leads to an underlying stochastic ordinary differential equation, the drift coefficient of which is typically not globally one-sided Lipschitz continuous. We investigate a half-explicit, drift-truncated Euler scheme that fulfills the constraint exactly. Pathwise uniform $L_p$-convergence is established. The proof is based on a suitable decomposition of the discrete Lagrange multipliers and on norm estimates for the single components, enabling the verification of consistency, semistability and moment growth properties of the scheme.