2016/01/09 by David R. Kelly, Eric Vanden‐Eijnden, Kelly, David +1
Computer Science · Physics and Astronomy · #34E13 #60F10 #70K70 #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1601.02147
openalex publication_date 2016/01/09 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the\nslow variables in fast-slow systems is investigated. In particular, it is shown\nvia analysis of central limit theorems (CLT) and large deviation principles\n(LDP) that the standard version of HMM artificially amplifies these\nfluctuations. A simple modification of HMM, termed parallel HMM, is introduced\nand is shown to remedy this problem, capturing fluctuations correctly both at\nthe level of the CLT and the LDP. Similar type of arguments can also be used to\njustify that the tau-leaping method used in the context of Gillespie's\nstochastic simulation algorithm for Markov jump processes also captures the\nright CLT and LDP for these processes.\n