TY - JOUR

T1 - Fluctuations in the heterogeneous multiscale methods for fast–slow systems

AU - Kelly, David

AU - Vanden-Eijnden, Eric

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/12/1

Y1 - 2017/12/1

N2 - How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast–slow systems is investigated. In particular, it is shown via analysis of central limit theorem (CLT) and large deviation principle (LDP) that the standard version of HMM artificially amplifies these fluctuations. A simple modification of HMM, termed parallel HMM, is introduced and is shown to remedy this problem, capturing fluctuations correctly both at the level of the CLT and the LDP. All results in this article assume the HMM speedup factor λ to be constant and in particular independent of the scale parameter ε. Similar type of arguments can also be used to justify that the τ-leaping method used in the context of Gillespie’s stochastic simulation algorithm for Markov jump processes also captures the right CLT and LDP for these processes.

AB - How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast–slow systems is investigated. In particular, it is shown via analysis of central limit theorem (CLT) and large deviation principle (LDP) that the standard version of HMM artificially amplifies these fluctuations. A simple modification of HMM, termed parallel HMM, is introduced and is shown to remedy this problem, capturing fluctuations correctly both at the level of the CLT and the LDP. All results in this article assume the HMM speedup factor λ to be constant and in particular independent of the scale parameter ε. Similar type of arguments can also be used to justify that the τ-leaping method used in the context of Gillespie’s stochastic simulation algorithm for Markov jump processes also captures the right CLT and LDP for these processes.

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U2 - 10.1186/s40687-017-0112-2

DO - 10.1186/s40687-017-0112-2

M3 - Article

AN - SCOPUS:85050372427

VL - 4

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

SN - 2522-0144

IS - 1

M1 - 23

ER -