2014/06/08 by Álvaro Moraes, Raúl Tempone, Moraes, Alvaro +3
Biochemistry, Genetics and Molecular Biology · Energy · Materials Science · #Catalytic Processes in Materials Science #Electrocatalysts for Energy Conversion #FOS: Mathematics #Gene Regulatory Network Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1406.1989
openalex publication_date 2014/06/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Stochastic modeling of reaction networks is a framework used to describe the\ntime evolution of many natural and artificial systems, including, biochemical\nreactive systems at the molecular level, viral kinetics, the spread of epidemic\ndiseases, and wireless communication networks, among many other examples. In\nthis work, we present a novel multilevel Monte Carlo method for kinetic\nsimulation of stochastic reaction networks that is specifically designed for\nsystems in which the set of reaction channels can be adaptively partitioned\ninto two subsets characterized by either "high" or "low" activity. Adaptive in\nthis context means that the partition evolves in time according to the states\nvisited by the stochastic paths of the system. To estimate expected values of\nobservables of the system at a prescribed final time, our method bounds the\nglobal computational error to be below a prescribed tolerance, TOL, within a\ngiven confidence level. This is achieved with a computational complexity of\norder O(TOL-2), the same as with an exact method, but with a smaller\nconstant. We also present a novel control variate technique based on the\nstochastic time change representation by Kurtz, which may dramatically reduce\nthe variance of the coarsest level at a negligible computational cost. Our\nnumerical examples show substantial gains with respect to the standard\nStochastic Simulation Algorithm (SSA) by Gillespie and also our previous hybrid\nChernoff tau-leap method.\n