Drift-preserving numerical integrators for stochastic Hamiltonian systems
Chuchu Chen, David Cohen, Raffaele D’Ambrosio, Annika Lang
Abstract
Abstract The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.
Topics & Concepts
IntegratorMathematicsApplied mathematicsEstimatorNonlinear systemNumerical analysisHamiltonian (control theory)Separable spaceHamiltonian systemMonte Carlo methodConvergence (economics)Mathematical optimizationMathematical analysisComputer sciencePhysicsEconomicsStatisticsComputer networkEconomic growthBandwidth (computing)Quantum mechanicsNumerical methods for differential equationsStochastic processes and financial applicationsAdvanced Numerical Methods in Computational Mathematics