2019/01/22 by Przemysław Zieliński, Hannes Vandecasteele, Zieliński, Przemysław +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H35 #62E17 #65C05 #65L20 #94A17 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1901.07405
openalex publication_date 2019/01/22 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
We analyse the convergence and stability of a micro-macro acceleration\nalgorithm for Monte Carlo simulations of stiff stochastic differential\nequations with a time-scale separation between the fast evolution of the\nindividual stochastic realizations and some slow macroscopic state variables of\nthe process. The micro-macro acceleration method performs a short simulation of\na large ensemble of individual fast paths, before extrapolating the macroscopic\nstate variables of interest over a larger time step. After extrapolation, the\nmethod constructs a new probability distribution that is consistent with the\nextrapolated macroscopic state variables, while minimizing Kullback-Leibler\ndivergence with respect to the distribution available at the end of the Monte\nCarlo simulation. In the current work, we study the convergence and stability\nof this method on linear stochastic differential equations with additive noise,\nwhen only extrapolating the mean of the slow component. For this case, we prove\nconvergence to the microscopic dynamics when the initial distribution is\nGaussian and present a stability result for non-Gaussian initial laws.\n