메뉴 건너뛰기




Volumn 10, Issue 4, 2012, Pages 1493-1524

Weak error analysis of numerical methods for stochastic models of population processes

Author keywords

Computational complexity; Continuous time Markov chain; Gillespie's algorithm; Multiscale; Reaction network; Tau leaping; Weak error

Indexed keywords

ANALYTICAL RESULTS; APPROXIMATE METHODS; CELL BIOLOGY; CONTINUOUS TIME MARKOV CHAIN; ENSEMBLE AVERAGES; EXPECTED VALUES; MULTISCALES; NUMERICAL APPROXIMATIONS; REACTION NETWORK; SAMPLE PATH; SCALINGS; STEP SIZE; TAU-LEAPING;

EID: 84871839910     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/110849699     Document Type: Article
Times cited : (19)

References (28)
  • 1
    • 36849077107 scopus 로고    scopus 로고
    • A modified next reaction method for simulating chemical systems with time dependent propensities and delays
    • D. F. Anderson, A modified next reaction method for simulating chemical systems with time dependent propensities and delays, J. Chem. Phys., 127 (2007), 214107.
    • (2007) J. Chem. Phys , vol.127 , pp. 214107
    • Anderson, D.F.1
  • 2
    • 42649105096 scopus 로고    scopus 로고
    • Incorporating postleap checks in tau-leaping
    • D. F. Anderson, Incorporating postleap checks in tau-leaping, J. Chem. Phys., 128 (2008), 054103.
    • (2008) J. Chem. Phys , vol.128 , pp. 054103
    • Anderson, D.F.1
  • 3
    • 79957948210 scopus 로고    scopus 로고
    • Error analysis of tau-leap simulation methods
    • D. F. Anderson, A. Ganguly, and T. G. Kurtz, Error analysis of tau-leap simulation methods, Ann. Appl. Probab., 21 (2011), pp. 2226-2262.
    • (2011) Ann. Appl. Probab , vol.21 , pp. 2226-2262
    • Anderson, D.F.1    Ganguly, A.2    Kurtz, T.G.3
  • 4
    • 84861518013 scopus 로고    scopus 로고
    • Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics
    • D. F. Anderson and D. J. Higham, Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics, Multiscale Model. Simul., 10 (2012), pp. 146-179.
    • (2012) Multiscale Model. Simul , vol.10 , pp. 146-179
    • Anderson, D.F.1    Higham, D.J.2
  • 6
    • 78049309393 scopus 로고    scopus 로고
    • A weak trapezoidal method for a class of stochastic differential equations
    • D. F. Anderson and J. C. Mattingly, A weak trapezoidal method for a class of stochastic differential equations, Commun. Math. Sci., 9 (2011), pp. 301-318.
    • (2011) Commun. Math. Sci , vol.9 , pp. 301-318
    • Anderson, D.F.1    Mattingly, J.C.2
  • 7
    • 33744775760 scopus 로고    scopus 로고
    • Asymptotic analysis of multiscale approximations to reaction networks
    • K. Ball, T. G. Kurtz, L. Popovic, and G. Rempala, Asymptotic analysis of multiscale approximations to reaction networks, Ann. Appl. Probab., 16 (2006), pp. 1925-1961.
    • (2006) Ann. Appl. Probab , vol.16 , pp. 1925-1961
    • Ball, K.1    Kurtz, T.G.2    Popovic, L.3    Rempala, G.4
  • 8
    • 23944491675 scopus 로고    scopus 로고
    • Avoiding negative populations in explicit Poisson tau-leaping
    • Y. Cao, D. T. Gillespie, and L. R. Petzold, Avoiding negative populations in explicit Poisson tau-leaping, J. Chem. Phys., 123 (2005), 054104.
    • (2005) J. Chem. Phys , vol.123 , pp. 054104
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.R.3
  • 9
    • 22944480262 scopus 로고    scopus 로고
    • The slow-scale stochastic simulation algorithm
    • Y. Cao, D. T. Gillespie, and L. R. Petzold, The slow-scale stochastic simulation algorithm, J. Chem. Phys., 122 (2005), 014116.
    • (2005) J. Chem. Phys , vol.122 , pp. 014116
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.R.3
  • 10
    • 31544465969 scopus 로고    scopus 로고
    • Efficient step size selection for the tau-leaping simulation method
    • Y. Cao, D. T. Gillespie, and L. R. Petzold, Efficient step size selection for the tau-leaping simulation method, J. Chem. Phys., 124 (2006), 044109.
    • (2006) J. Chem. Phys , vol.124 , pp. 044109
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.R.3
  • 11
    • 34249936476 scopus 로고    scopus 로고
    • Trapezoidal tau-leaping formula for the stochastic simulation of biochemical system
    • in (FOSBE) 2005, Santa Barbara, CA
    • Y. Cao and L. R. Petzold, Trapezoidal tau-leaping formula for the stochastic simulation of biochemical system, in Proceedings of Foundations of Systems Biology in Engineering (FOSBE) 2005, Santa Barbara, CA, 2005, pp. 149-152.
    • (2005) Proceedings of Foundations of Systems Biology in Engineering , pp. 149-152
    • Cao, Y.1    Petzold, L.R.2
  • 12
    • 22944469465 scopus 로고    scopus 로고
    • Binomial distribution based τ-leap accelerated stochastic simulation
    • A. Chatterjee and D. G. Vlachos, Binomial distribution based τ-leap accelerated stochastic simulation, J. Chem. Phys., 122 (2005), 024112.
    • (2005) J. Chem. Phys , vol.122 , pp. 024112
    • Chatterjee, A.1    Vlachos, D.G.2
  • 13
    • 27744516835 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
    • W. E, D. Liu, and E. Vanden-Eijnden, Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates, J. Chem. Phys., 123 (2005), 194107.
    • (2005) J. Chem. Phys , vol.123 , pp. 194107
    • Liu, W.E.D.1    Vanden-Eijnden, E.2
  • 15
    • 21444438810 scopus 로고    scopus 로고
    • A stochastic analysis of first-order reaction networks
    • C. Gadgil, C. H. Lee, and H. G. Othmer, A stochastic analysis of first-order reaction networks, Bull. Math. Biol., 67 (2005), pp. 901-946.
    • (2005) Bull. Math. Biol , vol.67 , pp. 901-946
    • Gadgil, C.1    Lee, C.H.2    Othmer, H.G.3
  • 16
    • 0001144902 scopus 로고    scopus 로고
    • Efficient exact stochastic simulation of chemical systems with many species and many channels
    • M. Gibson and J. Bruck, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A, 105 (2000), pp. 1876-1889.
    • (2000) J. Phys. Chem. A , vol.105 , pp. 1876-1889
    • Gibson, M.1    Bruck, J.2
  • 17
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • D. T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22 (1976), pp. 403-434.
    • (1976) J. Comput. Phys , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 18
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), pp. 2340-2361.
    • (1977) J. Phys. Chem , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 19
    • 0035933994 scopus 로고    scopus 로고
    • Approximate accelerated simulation of chemically reaction systems
    • D. T. Gillespie, Approximate accelerated simulation of chemically reaction systems, J. Chem. Phys., 115 (2001), pp. 1716-1733.
    • (2001) J. Chem. Phys , vol.115 , pp. 1716-1733
    • Gillespie, D.T.1
  • 20
    • 0242425970 scopus 로고    scopus 로고
    • Improved leap-size selection for accelerated stochastic simulation
    • D. T. Gillespie and L. R. Petzold, Improved leap-size selection for accelerated stochastic simulation, J. Chem. Phys., 119 (2003), pp. 8229-8234.
    • (2003) J. Chem. Phys , vol.119 , pp. 8229-8234
    • Gillespie, D.T.1    Petzold, L.R.2
  • 21
    • 0024478825 scopus 로고
    • A GSMP formalism for discrete event systems
    • P. W. Glynn, A GSMP formalism for discrete event systems, Proc. IEEE, 77 (1989), pp. 14-23.
    • (1989) Proc. IEEE , vol.77 , pp. 14-23
    • Glynn, P.W.1
  • 22
    • 79961222409 scopus 로고    scopus 로고
    • The weak convergence analysis of tau-leaping methods: Revisited
    • Y. Hu, T. Li, and B. Min, The weak convergence analysis of tau-leaping methods: Revisited, Commun. Math. Sci., 9 (2011), pp. 965-996.
    • (2011) Commun. Math. Sci , vol.9 , pp. 965-996
    • Hu, Y.1    Li, T.2    Min, B.3
  • 23
    • 79960552585 scopus 로고    scopus 로고
    • A weak second order tau-leaping scheme for simulating chemical reaction systems
    • Y. Hu, T. Li, and B. Min, A weak second order tau-leaping scheme for simulating chemical reaction systems, J. Chem. Phys., 135 (2011), 024113.
    • (2011) J. Chem. Phys , vol.135 , pp. 024113
    • Hu, Y.1    Li, T.2    Min, B.3
  • 24
    • 81255158896 scopus 로고    scopus 로고
    • Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
    • M. Hutzenthaler and A. Jentzen, Convergence of the stochastic Euler scheme for locally Lipschitz coefficients, Found. Comput. Math., 11 (2011), pp. 657-706.
    • (2011) Found. Comput. Math , vol.11 , pp. 657-706
    • Hutzenthaler, M.1    Jentzen, A.2
  • 25
    • 84871828134 scopus 로고    scopus 로고
    • Separation of time-scales and model reduction for stochastic reaction networks
    • to appear; available online from
    • H.-W. Kang and T. G. Kurtz, Separation of time-scales and model reduction for stochastic reaction networks. Ann. Appl. Probab., to appear; available online from http://www. imstat.org/aap/future papers.html.
    • Ann. Appl. Probab.
    • Kang, H.-W.1    Kurtz, T.G.2
  • 26
    • 0003335723 scopus 로고
    • Numerical solution of stochastic differential equations
    • (N. Y.), Springer-Verlag, Berlin
    • P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Appl. Math. (N. Y.) 23, Springer-Verlag, Berlin, 1992.
    • (1992) Appl. Math. , vol.23
    • Kloeden, P.E.1    Platen, E.2
  • 27
  • 28
    • 34247560632 scopus 로고    scopus 로고
    • An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability
    • H. Lambda, J. C. Mattingly, and A. M. Stuart, An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability, IMA J. Numer. Anal., 27 (2007), pp. 479-506.
    • (2007) IMA J. Numer. Anal , vol.27 , pp. 479-506
    • Lambda, H.1    Mattingly, J.C.2    Stuart, A.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.