Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions

Abstract

A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.

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Correspondence to David F. Anderson.

Additional information

Grant support from NSF-DMS-1318832 (Directorate for Mathematical and Physical Sciences) and Army Research Office Grant W911NF-14-1-0401.

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Anderson, D.F., Yuan, C. Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions. Bull Math Biol 81, 2902–2930 (2019). https://doi.org/10.1007/s11538-018-0430-6

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Keywords

  • Stochastic chemical kinetics
  • Variance reduction
  • Gillespie algorithm
  • Stochastic simulation
  • Non-homogeneous Markov chains