Vienna 2013: DJH Lectures. Some References

D J Higham, September, 2013 Here are some pointers to the literature. This is not intended to be a comprehensive list, and is biased towards my own research interests. Lecture 1, Gillespie: • [5, 6] are classic references for stochastic simulation, [10] gives a gentle introduction • [7] introduced tau-leaping, [1] gives a rigorous analysis • [17] covers modeling and simulation issues at various scales • [15] gives some analysis of mean hitting times

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

[2]  L. Szpruch,et al.  Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model , 2011 .

[3]  Peter E. Kloeden,et al.  Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations , 2011, 1105.0226.

[4]  Arnulf Jentzen,et al.  Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients , 2009, Found. Comput. Math..

[5]  David F. Anderson,et al.  Error analysis of tau-leap simulation methods , 2009, 0909.4790.

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

[7]  P. Kloeden,et al.  Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  LUKASZ SZPRUCH,et al.  Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations , 2010, Multiscale Model. Simul..

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

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

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

[12]  D. Higham,et al.  Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process , 2005 .

[13]  Andrew M. Stuart,et al.  Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations , 2002, SIAM J. Numer. Anal..

[14]  Stefan Heinrich,et al.  Multilevel Monte Carlo Methods , 2001, LSSC.

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