Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-03-30
Physics
Condensed Matter
Statistical Mechanics
21 pages (Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, A. Gorban, N. Kazantzis, Y. Kevrekidis, H.C
Scientific paper
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 \cite{ait2,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.
Calderon Christopher P.
Kevrekidis Ioannis G.
Provata Astero
Tsekouras Giorgos-Artemios
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