Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise
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[1] David F. Anderson,et al. Continuous Time Markov Chain Models for Chemical Reaction Networks , 2011 .
[2] David F. Anderson,et al. Error analysis of tau-leap simulation methods , 2009, 0909.4790.
[3] G. N. Milstein,et al. Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noises , 1997, SIAM J. Sci. Comput..
[4] Martin Braun. Differential equations and their applications , 1976 .
[5] Denis Belomestny,et al. Variance reduced multilevel path simulation: going beyond the complexity $\varepsilon^{-2}$ , 2014 .
[6] M. V. Tretyakov,et al. Stochastic Numerics for Mathematical Physics , 2004, Scientific Computation.
[7] Giovanni Conforti,et al. On small-noise equations with degenerate limiting system arising from volatility models , 2014, 1404.4464.
[8] Peter E. Kloeden,et al. Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations , 2011, 1105.0226.
[9] Lan Zhang,et al. A Tale of Two Time Scales , 2003 .
[10] S. Laughlin,et al. Ion-Channel Noise Places Limits on the Miniaturization of the Brain’s Wiring , 2005, Current Biology.
[11] D. Gillespie. The chemical Langevin equation , 2000 .
[12] Desmond J. Higham,et al. Complexity of Multilevel Monte Carlo Tau-Leaping , 2014, SIAM J. Numer. Anal..
[13] D. Gillespie. Markov Processes: An Introduction for Physical Scientists , 1991 .
[14] Sergei Petrovskii,et al. Noise-induced suppression of periodic travelling waves in oscillatory reaction–diffusion systems , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[15] D. E. Postnov,et al. Stochastic dynamics of FitzHugh-Nagumo model near the canard explosion , 2003, 2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775).
[16] H. Wio,et al. Exact nonequilibrium potential for the FitzHugh-Nagumo model in the excitable and bistable regimes , 1998 .
[17] Georg Denk,et al. Modelling and simulation of transient noise in circuit simulation , 2007 .
[18] Thomas Müller-Gronbach,et al. Deterministic Quadrature Formulas for SDEs Based on Simplified Weak Itô–Taylor Steps , 2016, Found. Comput. Math..
[19] Henry C. Tuckwell,et al. Determination of Firing Times for the Stochastic Fitzhugh-Nagumo Neuronal Model , 2003, Neural Computation.
[20] Xuerong Mao,et al. Stochastic differential equations and their applications , 1997 .
[21] Thomas G. Kurtz,et al. Stochastic Analysis of Biochemical Systems , 2015 .
[22] Desmond J. Higham,et al. Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics , 2011, Multiscale Model. Simul..
[23] Antoine Jacquier,et al. Large Deviations and Asymptotic Methods in Finance , 2015 .
[24] S. Tindel,et al. An analysis of a stochastic model for bacteriophage systems. , 2013, Mathematical biosciences.
[25] T. Faniran. Numerical Solution of Stochastic Differential Equations , 2015 .
[26] Mark D. McDonnell,et al. Channel-noise-induced stochastic facilitation in an auditory brainstem neuron model. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.
[27] Jürgen Kurths,et al. Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.
[28] Ilya Nemenman,et al. Speeding up Evolutionary Search by Small Fitness Fluctuations , 2010, Journal of statistical physics.
[29] G. A. Pavliotis,et al. Parameter Estimation for Multiscale Diffusions , 2007 .
[30] Boyce E. Griffith,et al. Multiscale temporal integrators for fluctuating hydrodynamics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.
[31] Michael B. Giles,et al. Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..
[32] Huu Tue Huynh,et al. Solution of Stochastic Differential Equations , 2012 .
[33] Michael V. Tretyakov,et al. Numerical Methods in the Weak Sense for Stochastic Differential Equations with Small Noise , 1997 .
[34] P. Kloeden,et al. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients , 2010, 1010.3756.