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. Bramson, M. D. (1983) Convergence of solutions of the Kolmogorov equation to travelling waves. Mem. Amer. Math. Soc., 285, 1--190. Math. Review 84m:60098
  2. Champneys, A., Harris, S., Toland, J., Warren, J. & Williams, D. (1995) Algebra, analysis and probability for a coupled system of reaction-diffusion equations. Phil. Trans. R. Soc. Lond., A 350, 69--112. Math. Review 96e:35080
  3. Dawson, D. A. (1993) Measure-valued Markov processes, Ecole d'Ete de Probabilites de Saint Flour, 1991, Lecture Notes in Mathematics, 1541. New York: Springer-Verlag. Math. Review 94m:60101
  4. Dunbar, S.R. (1988) A branching random evolution and a nonlinear hyperbolic equation. SIAM J. Appl. Math., 48, 1510--1526. Math. Review 90a:60183
  5. Dynkin, E. B. (1994) An Introduction to Branching Measure-Valued Processes. Providence, Rhode Island: American Mathematical Society. Math. Review 96f:60145
  6. Fisher, R. A. (1937) The wave of advance of an advantageous gene. Ann. Eugenics, 7, 353--369.
  7. Hadeler, K. P. (1995) Travelling Fronts in Random Walk Systems. Forma, 10, 223--233. Math. Review 98m:35098
  8. Holmes, E. E. (1993) Are diffusion models too simple? A comparison with telegraph models of invasion. Amer. Naturalist, 142, 779--795.
  9. Kolmogorov, A. N., Petrowski, I. & Piscounov, N. (1937) Etude de l'equation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique. Mosc. Univ. Bull. Math., 1, 1--25.
  10. Lyne, O.D. (2000) Travelling waves for a certain first-order coupled PDE system. Electron. J. Probab., 5, paper 14, 1--40. Math. Review 1781026
  11. Lyne, O.D. (1996) Probability and analysis for a hyperbolic coupled PDE system. Unpublished Ph.D. thesis, University of Bath.
  12. McKean, H. P. (1975) Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math., 28, 323--331. Math. Review 53 #4262
  13. McKean, H. P. (1976) Correction to the above. Comm. Pure Appl. Math., 29, 553--554. Math. Review 54 #11534
  14. Mitchell, A. R. & Griffiths, D. F. (1980) The Finite Difference Method in Partial Differential Equations. Chichester: Wiley Math. Review 82a:65002
  15. Neveu, J. (1987) Multiplicative martingales for spatial branching processes. Seminar on Stochastic Processes (ed. E. Cinlar, K. L Chung and R. K. Getoor), Progress in Probability and Statistics 15. pp. 223--241. Boston: Birkhauser. Math. Review 91f:60144
  16. Othmer, H. G., Dunbar, S. R. & Alt, W. (1988) Models of dispersion in biological systems. J. Math. Biol., 26, 263--298. Math. Review 90a:92064
  17. Rogers, L. C. G. & Williams, D. (1987) Diffusions, Markov Processes and Martingales, Volume 2: Ito Calculus. Chichester: Wiley. Math. Review 89k:60117
  18. Strikwerda, J. C. (1989) Finite Difference Schemes and Partial Differential Equations. Pacific Grove: Wadsworth & Brooks/Cole. Math. Review 90g:65004
Bookmark and Share


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