Multi-level Monte Carlo for stochastically modeled chemical kinetic systems

[1]  D. Higham Stochastic Ordinary Differential Equations in Applied and Computational Mathematics , 2011 .

[2]  Eric Renshaw,et al.  Stochastic Population Processes , 2011 .

[3]  K. A. Cliffe,et al.  Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients , 2011, Comput. Vis. Sci..

[4]  David F. Anderson,et al.  Continuous Time Markov Chain Models for Chemical Reaction Networks , 2011 .

[5]  W. Schachermayer,et al.  Multilevel quasi-Monte Carlo path simulation , 2009 .

[6]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[7]  David F. Anderson Incorporating postleap checks in tau-leaping. , 2007, The Journal of chemical physics.

[8]  M. Giles Improved Multilevel Monte Carlo Convergence using the Milstein Scheme , 2008 .

[9]  David F Anderson,et al.  A modified next reaction method for simulating chemical systems with time dependent propensities and delays. , 2007, The Journal of chemical physics.

[10]  D. Dubnau,et al.  Noise in Gene Expression Determines Cell Fate in Bacillus subtilis , 2007, Science.

[11]  Tiejun Li,et al.  Analysis of Explicit Tau-Leaping Schemes for Simulating Chemically Reacting Systems , 2007, Multiscale Model. Simul..

[12]  Darren J. Wilkinson Stochastic Modelling for Systems Biology , 2006 .

[13]  Linda R Petzold,et al.  Efficient step size selection for the tau-leaping simulation method. , 2006, The Journal of chemical physics.

[14]  T. Kurtz,et al.  Submitted to the Annals of Applied Probability ASYMPTOTIC ANALYSIS OF MULTISCALE APPROXIMATIONS TO REACTION NETWORKS , 2022 .

[15]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[16]  Benjamin B. Kaufmann,et al.  Contributions of low molecule number and chromosomal positioning to stochastic gene expression , 2005, Nature Genetics.

[17]  D. Gillespie,et al.  Avoiding negative populations in explicit Poisson tau-leaping. , 2005, The Journal of chemical physics.

[18]  D. Vlachos,et al.  Binomial distribution based tau-leap accelerated stochastic simulation. , 2005, The Journal of chemical physics.

[19]  Muruhan Rathinam,et al.  Consistency and Stability of Tau-Leaping Schemes for Chemical Reaction Systems , 2005, Multiscale Model. Simul..

[20]  K. Burrage,et al.  Binomial leap methods for simulating stochastic chemical kinetics. , 2004, The Journal of chemical physics.

[21]  J. Raser,et al.  Control of Stochasticity in Eukaryotic Gene Expression , 2004, Science.

[22]  J. Paulsson Summing up the noise in gene networks , 2004, Nature.

[23]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[24]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[25]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[26]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[27]  T. Kurtz Strong approximation theorems for density dependent Markov chains , 1978 .

[28]  D. Gillespie Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[29]  D. Gillespie A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[30]  T. Kurtz The Relationship between Stochastic and Deterministic Models for Chemical Reactions , 1972 .

[31]  D. A. Mcquarrie Stochastic approach to chemical kinetics , 1967, Journal of Applied Probability.