Free Access
Volume 10, September 2006
Page(s) 236 - 257
Published online 03 May 2006
  1. K.B. Athreya and P.E. Ney, Branching processes. Dover Publ. Inc. Mineola, NY (2004). [Google Scholar]
  2. L. Beghin, L. Nieddu and E. Orsingher, Probabilistic analysis of the telegrapher's process with drift by mean of relativistic transformations. J. Appl. Math. Stoch. Anal. 14 (2001) 11–25. [CrossRef] [Google Scholar]
  3. M. Bramson, Maximal displacement of branching Brownian motion. Comm. Pure Appl. Math. 31 (1978) 531–581. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves. Mem. Amer. Math. Soc. 44 (1983) iv+190. [Google Scholar]
  5. B. Chauvin and A. Rouault, Supercritical branching Brownian motion and K-P-P equation in the critical speed-are. Math. Nachr. 19 (1990) 41–59. [CrossRef] [Google Scholar]
  6. A. Di Crescenzo and F. Pellerey, On prices' evolutions based on geometric telegrapher's process. Appl. Stoch. Models Business Industry 18 (2002) 171–184. [CrossRef] [Google Scholar]
  7. S.R. Dunbar, A branching random evolution and a nonlinear hyperbolic equation. SIAM J. Appl. Math. 48 (1988) 1510–1526. [CrossRef] [MathSciNet] [Google Scholar]
  8. S.R. Dunbar and H.G. Othmer, On a nonlinear hyperbolic equation describing transmission lines, cell movement, and branching random walks, in Nonlinear oscillations in biology and chemistry, (Salt Lake City, Utah, 1985). Lect. Notes Biomath. 66 (1986) 274–289. [Google Scholar]
  9. R.A. Fisher, The advance of advantageous genes. Ann. Eugenics 7 (1937) 335–369. [Google Scholar]
  10. J. Fort and V. Mendez, Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment. Rep. Prog. Phys. 65 (2002) 895–954. [CrossRef] [Google Scholar]
  11. S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation. Quart. J. Mech. Apl. Math. 4 (1951) 129–156. [CrossRef] [MathSciNet] [Google Scholar]
  12. K.P. Hadeler, Nonlinear propagation in reaction transport systems. Differential equations with applications to biology, Halifax, NS, 1997, Fields Inst. Commun. 21 Amer. Math. Soc., Providence, RI (1999) 251–257. [Google Scholar]
  13. K.P. Hadeler, Reaction transport systems in biological modelling, In Mathematics inspiring by biology. Lect. Notes in Math. 1714 (1999) 95–150. [CrossRef] [Google Scholar]
  14. K.P. Hadeler, T. Hillen and F. Lutscher, The Langevin or Kramer approach to biological modelling. Math. Mod. Meth. Appl. Sci. 14 (2004) 1561–1583. [CrossRef] [Google Scholar]
  15. T. Hillen and H.G. Othmer, The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math. 61 (2000) 751–775. H.G. Othmer and T. Hillen, The diffusion limit of transport equations. II. Chemotaxis equations. SIAM J. Appl. Math. 62, (2002) 1222–1250. [CrossRef] [MathSciNet] [Google Scholar]
  16. W. Horsthemke, Spatial instabilities in reaction random walks with direction-independent kinetics. Phys. Rev. E 60 (1999) 2651–2663. [CrossRef] [MathSciNet] [Google Scholar]
  17. W. Horsthemke, Fisher waves in reaction random walks. Phys. Lett. A 263 (1999) 285–292. [CrossRef] [MathSciNet] [Google Scholar]
  18. D.D. Joseph and L. Preziosi, Heat waves. Rev. Mod. Phys. 61 (1989) 41–73. [CrossRef] [Google Scholar]
  19. D.D. Joseph and L. Preziosi, Addendum to the paper “Heat waves”. Rev. Mod. Phys. 62 (1990) 375–391. [CrossRef] [Google Scholar]
  20. M. Kac, Probability and related topics in physical sciences. Interscience, London (1959). [Google Scholar]
  21. M. Kac, A Stochastic model related to the telegraph equation. Rocky Mountain J. Math. 4 (1974) 497–509. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Kolmogorov, I. Petrovskii and N. Piskunov, Étude de l'équation de la diffusion avec croissance de la quantité de la matière et son application à un problème biologique. Bull. Math. 1 (1937) 1–25. [Google Scholar]
  23. O.D. Lyne, Travelling waves for a certain first-order coupled PDE system. Electronic J. Prob. 5 (2000) 1–40. [Google Scholar]
  24. O.D. Lyne and D. Williams, Weak solutions for a simple hyperbolic system. Electronic J. Prob. 6 (2001) 1–21. [Google Scholar]
  25. H.P. McKean, Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math. XXVIII (1975) 323–331. [Google Scholar]
  26. H.P. McKean, Correction to above. Comm. Pure Appl. Math. XXIX (1976) 553–554. [Google Scholar]
  27. S. Mizohata, The theory of partial differential equations. Cambridge University Press, New York (1973) xii+490. [Google Scholar]
  28. V. Mendez and J. Camacho, Dynamics and thermodynamics of delayed population growth. Phys. Rev. E 55 (1997) 6476–6482. [CrossRef] [Google Scholar]
  29. V. Mendez and A. Compte, Wavefronts in bistable hyperbolic reaction-diffusion systems. Physica A 260 (1998) 90–98. [CrossRef] [Google Scholar]
  30. M. Nagasawa, Schrödinger equations and diffusion theory. Monographs in Mathematics, Birkhäuser Verlag, Basel 86 (1993) pp. x+319. [Google Scholar]
  31. E. Orsingher, Probability law, flow function, maximum distribution of wave governed random motions and their connections with Kirchoff's laws. Stoch. Proc. Appl. 34 (1990) 49–66. [CrossRef] [Google Scholar]
  32. H.G. Othmer, S.R. Dunbar and W. Alt, Models of dispersal in biological systems. J. Math. Biol. 26 (1988) 263–298. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  33. M. Pinsky, Lectures on random evolution. World Scient. Publ. Co., River Edge, NY (1991). [Google Scholar]
  34. N.E. Ratanov, Telegraph processes with reflecting and absorbing barriers in inhomogeneous media. Theor. Math. Phys. 112 (1997) 857–865. [CrossRef] [Google Scholar]
  35. N. Ratanov, Reaction-advection random motions in inhomogeneous media. Physica D 189 (2004) 130–140. [CrossRef] [MathSciNet] [Google Scholar]
  36. N. Ratanov, Pricing options under telegraph processes. Rev. Econ. Ros. 8 (2005) 131–150. [Google Scholar]
  37. A.I. Volpert, V.A. Volpert and Vl.A. Volpert, Travelling wave solutions of parabolic systems. Translated from the Russian manuscript by James F. Heyda. Translations of Mathematical Monographs. 140 Amer. Math. Soc. Providence, RI, (1994) pp. xii+448. [Google Scholar]
  38. G.H. Weiss, Aspects and applications of the random walk. North-Holland, Amsterdam (1994). [Google Scholar]
  39. G.H. Weiss, Some applications of persistent random walks and the telegrapher's equation. Physica A 311 (2002) 381–410. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.