2006/03/30 by C. P. Calderon, George Tsekouras, Calderon, C. P. +7
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Innovation Diffusion and Forecasting #Statistical Mechanics (cond-mat.stat-mech) #Statistical Methods and Bayesian Inference #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0603817
21 pages (Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, A. Gorban, N. Kazantzis, Y. Kevrekidis, H.C. Ottinger, C. Theodoropoulos (Eds.), Springer, Berlin--Heidelberg--New York, 2006.)
arxiv created 2006/03/30 · openalex publication_date 2006/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When the output of an atomistic simulation (such as the Gillespie stochastic simulation algorithm, SSA) can be approximated as a diffusion process, we may be interested in the dynamic features of the deterministic (drift) component of this diffusion. We perform traditional scientific computing tasks (integration, steady state and closed orbit computation, and stability analysis) on such a drift component using a SSA simulation of the Cyclic Lotka-Volterra system as our illustrative example. The results of short bursts of appropriately initialized SSA simulations are used to fit local diffusion models using Ait-Sahalia's transition density expansions \citeait2,aitECO,aitVEC in a maximum likelihood framework. These estimates are then coupled with standard numerical algorithms (such as Newton-Raphson or numerical integration routines) to help design subsequent SSA experiments. A brief discussion of the validity of the local diffusion approximation of the SSA simulation (a jump process) is included.