Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations
For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility...