Free Access
Issue
ESAIM: PS
Volume 10, September 2006
Page(s) 236 - 257
DOI https://doi.org/10.1051/ps:2006009
Published online 03 May 2006
  1. K.B. Athreya and P.E. Ney, Branching processes. Dover Publ. Inc. Mineola, NY (2004).
  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]
  3. M. Bramson, Maximal displacement of branching Brownian motion. Comm. Pure Appl. Math. 31 (1978) 531–581. [CrossRef] [MathSciNet]
  4. M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves. Mem. Amer. Math. Soc. 44 (1983) iv+190.
  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]
  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]
  7. S.R. Dunbar, A branching random evolution and a nonlinear hyperbolic equation. SIAM J. Appl. Math. 48 (1988) 1510–1526. [CrossRef] [MathSciNet]
  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.
  9. R.A. Fisher, The advance of advantageous genes. Ann. Eugenics 7 (1937) 335–369.
  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]
  11. S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation. Quart. J. Mech. Apl. Math. 4 (1951) 129–156. [CrossRef] [MathSciNet]
  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.
  13. K.P. Hadeler, Reaction transport systems in biological modelling, In Mathematics inspiring by biology. Lect. Notes in Math. 1714 (1999) 95–150. [CrossRef]
  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]
  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]
  16. W. Horsthemke, Spatial instabilities in reaction random walks with direction-independent kinetics. Phys. Rev. E 60 (1999) 2651–2663. [CrossRef] [MathSciNet]
  17. W. Horsthemke, Fisher waves in reaction random walks. Phys. Lett. A 263 (1999) 285–292. [CrossRef] [MathSciNet]
  18. D.D. Joseph and L. Preziosi, Heat waves. Rev. Mod. Phys. 61 (1989) 41–73. [CrossRef]
  19. D.D. Joseph and L. Preziosi, Addendum to the paper “Heat waves”. Rev. Mod. Phys. 62 (1990) 375–391. [CrossRef]
  20. M. Kac, Probability and related topics in physical sciences. Interscience, London (1959).
  21. M. Kac, A Stochastic model related to the telegraph equation. Rocky Mountain J. Math. 4 (1974) 497–509. [CrossRef] [MathSciNet]
  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.
  23. O.D. Lyne, Travelling waves for a certain first-order coupled PDE system. Electronic J. Prob. 5 (2000) 1–40.
  24. O.D. Lyne and D. Williams, Weak solutions for a simple hyperbolic system. Electronic J. Prob. 6 (2001) 1–21.
  25. H.P. McKean, Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math. XXVIII (1975) 323–331.
  26. H.P. McKean, Correction to above. Comm. Pure Appl. Math. XXIX (1976) 553–554.
  27. S. Mizohata, The theory of partial differential equations. Cambridge University Press, New York (1973) xii+490.
  28. V. Mendez and J. Camacho, Dynamics and thermodynamics of delayed population growth. Phys. Rev. E 55 (1997) 6476–6482. [CrossRef]
  29. V. Mendez and A. Compte, Wavefronts in bistable hyperbolic reaction-diffusion systems. Physica A 260 (1998) 90–98. [CrossRef]
  30. M. Nagasawa, Schrödinger equations and diffusion theory. Monographs in Mathematics, Birkhäuser Verlag, Basel 86 (1993) pp. x+319.
  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]
  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]
  33. M. Pinsky, Lectures on random evolution. World Scient. Publ. Co., River Edge, NY (1991).
  34. N.E. Ratanov, Telegraph processes with reflecting and absorbing barriers in inhomogeneous media. Theor. Math. Phys. 112 (1997) 857–865. [CrossRef]
  35. N. Ratanov, Reaction-advection random motions in inhomogeneous media. Physica D 189 (2004) 130–140. [CrossRef] [MathSciNet]
  36. N. Ratanov, Pricing options under telegraph processes. Rev. Econ. Ros. 8 (2005) 131–150.
  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.
  38. G.H. Weiss, Aspects and applications of the random walk. North-Holland, Amsterdam (1994).
  39. G.H. Weiss, Some applications of persistent random walks and the telegrapher's equation. Physica A 311 (2002) 381–410. [CrossRef] [MathSciNet]

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