Variance Reduction with Array-RQMC for Tau-Leaping Simulation of Stochastic Biological and Chemical Reaction Networks

[1]  P. Marion,et al.  A Tool for Custom Construction of QMC and RQMC Point Sets , 2020, MCQMC.

[2]  Pierre L'Ecuyer,et al.  Array-RQMC for Option Pricing Under Stochastic Volatility Models , 2019, 2019 Winter Simulation Conference (WSC).

[3]  R. Baker,et al.  Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems , 2018, Bulletin of mathematical biology.

[4]  P. L’Ecuyer,et al.  Randomized quasi-Monte Carlo: An introduction for practitioners , 2016 .

[5]  Bruno Tuffin,et al.  Sorting methods and convergence rates for Array-RQMC: Some empirical comparisons , 2016, Math. Comput. Simul..

[6]  Pierre L'Ecuyer,et al.  Algorithm 958 , 2016, ACM Trans. Math. Softw..

[7]  Silvana Ilie,et al.  An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems , 2016 .

[8]  Michael B. Giles,et al.  Algorithm 955 , 2016, ACM Trans. Math. Softw..

[9]  Silvana Ilie,et al.  Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics. , 2015, The Journal of chemical physics.

[10]  Jae Kyoung Kim,et al.  The relationship between stochastic and deterministic quasi-steady state approximations , 2015, BMC Systems Biology.

[11]  P. L’Ecuyer,et al.  Algorithm 958: Lattice Builder: A General Software Tool for Constructing Rank-1 Lattice Rules , 2015, ACM Trans. Math. Softw..

[12]  N. Chopin,et al.  Sequential Quasi-Monte Carlo , 2014, 1402.4039.

[13]  Wonryull Koh,et al.  Improved spatial direct method with gradient-based diffusion to retain full diffusive fluctuations. , 2012, The Journal of chemical physics.

[14]  Pierre L'Ecuyer,et al.  Variance bounds and existence results for randomly shifted lattice rules , 2012, J. Comput. Appl. Math..

[15]  Philipp Thomas,et al.  The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions , 2012, BMC Systems Biology.

[16]  Desmond J. Higham,et al.  Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics , 2011, Multiscale Model. Simul..

[17]  Pierre L'Ecuyer,et al.  American option pricing with randomized quasi-Monte Carlo simulations , 2010, Proceedings of the 2010 Winter Simulation Conference.

[18]  F. Pillichshammer,et al.  Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration , 2010 .

[19]  C. Lemieux Monte Carlo and Quasi-Monte Carlo Sampling , 2009 .

[20]  Pierre L'Ecuyer,et al.  Quasi-Monte Carlo methods with applications in finance , 2008, Finance Stochastics.

[21]  P. L’Ecuyer,et al.  On Array-RQMC for Markov Chains: Mapping Alternatives and Convergence Rates , 2008 .

[22]  Frances Y. Kuo,et al.  Constructing Sobol Sequences with Better Two-Dimensional Projections , 2008, SIAM J. Sci. Comput..

[23]  Desmond J. Higham,et al.  Modeling and Simulating Chemical Reactions , 2008, SIAM Rev..

[24]  Andreas Hellander,et al.  Efficient computation of transient solutions of the chemical master equation based on uniformization and quasi-Monte Carlo. , 2008, The Journal of chemical physics.

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

[26]  Bruno Tuffin,et al.  Rare events, splitting, and quasi-Monte Carlo , 2007, TOMC.

[27]  Pierre L'Ecuyer,et al.  A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains , 2006, Oper. Res..

[28]  Pierre L'Ecuyer,et al.  Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces , 2006 .

[29]  Henryk Wozniakowski,et al.  Good Lattice Rules in Weighted Korobov Spaces with General Weights , 2006, Numerische Mathematik.

[30]  Pierre L'Ecuyer,et al.  Simulation in Java with SSJ , 2005, Proceedings of the Winter Simulation Conference, 2005..

[31]  Art B. Owen,et al.  Variance with alternative scramblings of digital nets , 2003, TOMC.

[32]  C. Rao,et al.  Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm , 2003 .

[33]  Fred J. Hickernell,et al.  Monte Carlo and Quasi-Monte Carlo Methods 2000 , 2002 .

[34]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[35]  D. Gillespie Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[36]  D. Gillespie The chemical Langevin equation , 2000 .

[37]  Fred J. Hickernell,et al.  Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature , 2000, SIAM J. Sci. Comput..

[38]  P. L’Ecuyer,et al.  Variance Reduction via Lattice Rules , 1999 .

[39]  Jirí Matousek,et al.  On the L2-Discrepancy for Anchored Boxes , 1998, J. Complex..

[40]  P. Hellekalek,et al.  Random and Quasi-Random Point Sets , 1998 .

[41]  C. Lécot,et al.  A Quasi-Monte Carlo Scheme Using Nets for a Linear Boltzmann Equation , 1998 .

[42]  A. Owen Monte Carlo Variance of Scrambled Net Quadrature , 1997 .

[43]  A. Owen Scrambled net variance for integrals of smooth functions , 1997 .

[44]  I. Sloan Lattice Methods for Multiple Integration , 1994 .

[45]  W. J. Anderson Continuous-Time Markov Chains: An Applications-Oriented Approach , 1991 .

[46]  P. Glynn,et al.  Discrete-time conversion for simulating finite-horizon Markov processes , 1990 .

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

[48]  A. Abas The calculation of the solution of multidimensional integral equations with methods Monte Carlo and quasi-Monte Carlo , 2021, T-Comm.

[49]  P. L’Ecuyer,et al.  On Figures of Merit for Randomly-Shifted Lattice Rules , 2012 .

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

[51]  Alexander Keller,et al.  Efficient Simultaneous Simulation of Markov Chains , 2008 .

[52]  Pierre L’Ecuyer,et al.  Random Number Generation , 2008, Encyclopedia of Algorithms.

[53]  Pierre L'Ecuyer,et al.  Randomized Quasi-Monte Carlo Simulation of Markov Chains with an Ordered State Space , 2006 .

[54]  P. L’Ecuyer,et al.  A COMBINATION OF RANDOMIZED QUASI-MONTE CARLO WITH SPLITTING FOR RARE-EVENT SIMULATION , 2005 .

[55]  Linda R Petzold,et al.  The slow-scale stochastic simulation algorithm. , 2005, The Journal of chemical physics.

[56]  Pierre L'Ecuyer,et al.  Recent Advances in Randomized Quasi-Monte Carlo Methods , 2002 .

[57]  F. J. Hickernell Obtaining O( N - 2+∈ ) Convergence for Lattice Quadrature Rules , 2002 .

[58]  Ferenc Szidarovszky,et al.  Modeling uncertainty : an examination of stochastic theory, methods, and applications , 2002 .

[59]  D. Pollock Smoothing with Cubic Splines , 1999 .

[60]  Pierre L'Ecuyer,et al.  Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators , 1999, Oper. Res..

[61]  Art B. Owen,et al.  Latin supercube sampling for very high-dimensional simulations , 1998, TOMC.

[62]  F. J. Hickernell Lattice rules: how well do they measure up? in random and quasi-random point sets , 1998 .

[63]  J. M. Sek,et al.  On the L2-discrepancy for anchored boxes , 1998 .

[64]  P. Kloeden,et al.  Numerical Solutions of Stochastic Differential Equations , 1995 .

[65]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[66]  W. J. Anderson Continuous-Time Markov Chains , 1991 .

[67]  I. Sobol On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .