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

References

  1. Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085 (88a:60130) Math. Review 88a:60130
  2. Feller, William. Generalized second order differential operators and their lateral conditions. Illinois J. Math. 1 (1957), 459--504. MR0092046 (19,1052c) Math. Review MR0092046
  3. Freidlin, Mark. Functional integration and partial differential equations. Annals of Mathematics Studies, 109. Princeton University Press, Princeton, NJ, 1985. x+545 pp. ISBN: 0-691-08354-1; 0-691-08362-2 MR0833742 (87g:60066) Math. Review 87g:60066
  4. Freidlin, Mark. Markov processes and differential equations: asymptotic problems. Lectures in Mathematics ETH Zurich. Birkhauser Verlag, Basel, 1996. vi+153 pp. ISBN: 3-7643-5392-9 MR1399081 (97f:60150) Math. Review 97f:60150
  5. Freidlin, Mark; Spiliopoulos, Konstantinos. Reaction-diffusion equations with nonlinear boundary conditions in narrow domains. Asymptot. Anal. 59 (2008), no. 3-4, 227--249. MR2450360 (Review) Math. Review MR2450360
  6. Freidlin, M. I.; Wentzell, A. D. Random perturbations of dynamical systems. Translated from the 1979 Russian original by Joseph Szucs. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 260. Springer-Verlag, New York, 1998. xii+430 pp. ISBN: 0-387-98362-7 MR1652127 (99h:60128) Math. Review 99h:60128
  7. Freidlin, Mark I.; Wentzell, Alexander D. Random perturbations of Hamiltonian systems. Mem. Amer. Math. Soc. 109 (1994), no. 523, viii+82 pp. MR1201269 (94j:35064) Math. Review 94j:35064
  8. Freidlin, Mark I.; Wentzell, Alexander D. Diffusion processes on graphs and the averaging principle. Ann. Probab. 21 (1993), no. 4, 2215--2245. MR1245308 (94j:60116) Math. Review 94j:60116
  9. Freidlin, Mark I.; Wentzell, Alexander D. Necessary and sufficient conditions for weak convergence of one-dimensional Markov processes. The Dynkin Festschrift, 95--109, Progr. Probab., 34, Birkhauser Boston, Boston, MA, 1994. MR1311713 (96b:60204) Math. Review 96b:60204
  10. Kim, Hyejin. On continuous dependence of solution of parabolic equations on coefficients. Asymptot. Anal. 62 (2009), no. 3-4, 147--162. MR2521761 Math. Review MR2521761
  11. Has?minskii, R. Z. Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations. (Russian) Teor. Verojatnost. i Primenen. 5 1960 196--214. MR0133871 (24 #A3695) Math. Review MR0133871
  12. 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 (92h:60127) Math. Review 92h:60127
  13. Mandl, Petr. Analytical treatment of one-dimensional Markov processes. Die Grundlehren der mathematischen Wissenschaften, Band 151 Academia Publishing House of the Czechoslovak Academy of Sciences, Prague; Springer-Verlag New York Inc., New York 1968 xx+192 pp. MR0247667 (40 #930) Math. Review MR0247667
  14. Rosenkrantz, Walter A. Limit theorems for solutions to a class of stochastic differential equations. Indiana Univ. Math. J. 24 (1974/75), 613--625. MR0368143 (51 #4385) Math. Review MR0368143
  15. Stroock, Daniel W.; Varadhan, S. R. Srinivasa. Multidimensional diffusion processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 233. Springer-Verlag, Berlin-New York, 1979. xii+338 pp. ISBN: 3-540-90353-4 MR0532498 (81f:60108) Math. Review 81f:60108
Bookmark and Share


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