The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Cerrai, Sandra. A Khasminskii type averaging principle for stochastic reaction-diffusion equations. Ann. Appl. Probab. 19 (2009), no. 3, 899--948. MR2537194
  • M. Galtier and G. Wainrib, Multiscale analysis of slow-fast neuronal learning models with noise., The Journal of Mathematical Neurosciences, 2,13 (2012).
  • Givon, Dror. Strong convergence rate for two-time-scale jump-diffusion stochastic differential systems. Multiscale Model. Simul. 6 (2007), no. 2, 577--594 (electronic). MR2338495
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • R.Z. Khas'~minskii, The averaging principle for stochastic differential equations, Problemy Peredachi Informatsii 4 (1968), no. 2, 86--87.
  • Kifer, Yuri. Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging. Mem. Amer. Math. Soc. 201 (2009), no. 944, viii+129 pp. ISBN: 978-0-8218-4425-0 MR2547839
  • Liu, Di. Strong convergence of principle of averaging for multiscale stochastic dynamical systems. Commun. Math. Sci. 8 (2010), no. 4, 999--1020. MR2744917
  • Lorenzi, Luca; Lunardi, Alessandra; Zamboni, Alessandro. Asymptotic behavior in time periodic parabolic problems with unbounded coefficients. J. Differential Equations 249 (2010), no. 12, 3377--3418. MR2737435
  • Papanicolaou, George C. Some probabilistic problems and methods in singular perturbations. Summer Research Conference on Singular Perturbations: Theory and Applications (Northern Arizona Univ., Flagstaff, Ariz., 1975). Rocky Mountain J. Math. 6 (1976), no. 4, 653--674. MR0431378
  • Veretennikov, A. Yu. On large deviations in the averaging principle for stochastic differential equations with periodic coefficients. II. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991), no. 4, 691--715; translation in Math. USSR-Izv. 39 (1992), no. 1, 677--701 MR1137583
  • Veretennikov, A. Yu. On an averaging principle for systems of stochastic differential equations. (Russian) Mat. Sb. 181 (1990), no. 2, 256--268; translation in Math. USSR-Sb. 69 (1991), no. 1, 271--284 MR1046602
  • G. Wainrib, Noise-controlled dynamics through the averaging principle for stochastic slow-fast systems., Phys. Rev. E (2011).
  • G. Wainrib; M. Thieullen; K. Pakdaman, Reduction of stochastic conductance-based neuron models with time-scales separation. J. Comput. Neurosci. 32 (2012), no. 2, 327--346. MR2904337
  • E, Weinan; Liu, Di; Vanden-Eijnden, Eric. Analysis of multiscale methods for stochastic differential equations. Comm. Pure Appl. Math. 58 (2005), no. 11, 1544--1585. MR2165382

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.