Lagrangian Quadrature Schemes for Computing Weak Solutions of Quantum Stochastic Differential Equations

Abstract

Lagrangian quadrature schemes for computing weak solutions of Lipschitzian quantum stochastic differential equations are introduced and studied. This is accomplished within the framework of the Hudson--Parthasarathy formulation of quantum stochastic calculus and subject to matrix elements of solution being sufficiently differentiable. Results concerning convergence of these schemes in the topology of the locally convex space of solution are presented. Numerical examples are given.