@article{AIHPB_2006__42_1_125_0, author = {Harris, J. W. and Harris, S. C. and Kyprianou, A. E.}, title = {Further probabilistic analysis of the {Fisher-Kolmogorov-Petrovskii-Piscounov} equation : one sided travelling-waves}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {125--145}, publisher = {Elsevier}, volume = {42}, number = {1}, year = {2006}, doi = {10.1016/j.anihpb.2005.02.005}, zbl = {1093.60059}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.005/} }
TY - JOUR AU - Harris, J. W. AU - Harris, S. C. AU - Kyprianou, A. E. TI - Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation : one sided travelling-waves JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2006 SP - 125 EP - 145 VL - 42 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.005/ DO - 10.1016/j.anihpb.2005.02.005 LA - en ID - AIHPB_2006__42_1_125_0 ER -
%0 Journal Article %A Harris, J. W. %A Harris, S. C. %A Kyprianou, A. E. %T Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation : one sided travelling-waves %J Annales de l'I.H.P. Probabilités et statistiques %D 2006 %P 125-145 %V 42 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.005/ %R 10.1016/j.anihpb.2005.02.005 %G en %F AIHPB_2006__42_1_125_0
Harris, J. W.; Harris, S. C.; Kyprianou, A. E. Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation : one sided travelling-waves. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 125-145. doi : 10.1016/j.anihpb.2005.02.005. http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.005/
[1] Nonlinear diffusions in population genetics, combustion and nerve propagation, in: (Ed.), Partial Differential Equations and Related Topics, Lecture Notes in Math., vol. 446, Springer-Verlag, Berlin, 1975. | MR | Zbl
, ,[2] Change of measures for Markov chains and the theorem for branching processes, Bernoulli 6 (2) (2000) 323-338. | MR | Zbl
,[3] Measure change in multitype branching, Adv. Appl. Probab. 36 (2) (2004) 544-581. | MR | Zbl
, ,[4] Handbook of Brownian Motion-Facts and Formulae, Probability and its Applications, Birkhäuser, Basel, 1996. | Zbl
, ,[5] Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math. 31 (5) (1978) 531-581. | MR | Zbl
,[6] Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc. 44 (285) (1983), iv+190. | MR | Zbl
,[7] Algebra, analysis and probability for a coupled system of reaction-diffusion equations, Philos. Trans. Roy. Soc. London 350 (1995) 69-112. | MR | Zbl
, , , , ,[8] Product martingales and stopping lines for branching Brownian motion, Ann. Probab. 19 (3) (1991) 1195-1205. | MR | Zbl
,[9] KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees, Probab. Theory Related Fields 80 (2) (1988) 299-314. | MR | Zbl
, ,[10] Supercritical branching Brownian motion and K-P-P equation in the critical speed-area, Math. Nachr. 149 (1990) 41-59. | MR | Zbl
, ,[11] Theory of Ordinary Differential Equations, McGraw-Hill Book Company, New York, 1955. | MR | Zbl
, ,[12] Superprocesses and partial differential equations, Ann. Probab. 21 (3) (1993) 1185-1262. | MR | Zbl
,[13] Local extinction versus local exponential growth for spatial branching processes, Ann. Probab. 32 (1A) (2004) 78-99. | MR | Zbl
, ,[14] The advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369. | JFM | MR
,[15] Functional Integration and Partial Differential Equations, Ann. Math. Stud., vol. 109, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl
,[16] Y. Git, J.W. Harris, S.C. Harris, Exponential growth-rates and large deviations for a typed branching diffusion, University of Bath preprint, 2004. | Zbl
[17] R. Hardy, S.C. Harris, A new formulation of the spine approach, University of Bath preprint, 2004.
[18] Travelling-waves for the FKPP equation via probabilistic arguments, Proc. Roy. Soc. Edinburgh Sect. A 129 (3) (1999) 503-517. | MR | Zbl
,[19] Large deviations and martingales for a typed branching diffusion. I, Astérisque 236 (1996) 133-154, Hommage à P.A. Meyer et J. Neveu. | Numdam | MR | Zbl
, ,[20] Branching Markov processes. I, J. Math. Kyoto Univ. 8 (1968) 233-278. | MR | Zbl
, , ,[21] Branching Markov processes. II, J. Math. Kyoto Univ. 8 (1968) 365-410. | MR | Zbl
, , ,[22] Branching Markov processes. III, J. Math. Kyoto Univ. 9 (1969) 95-160. | MR | Zbl
, , ,[23] On the nonlinear diffusion equation of Kolmogorov-Petrovskii-Piskunov type, Osaka J. Math. 13 (1) (1976) 11-66. | MR | Zbl
,[24] Branching Brownian motion with absorption, Stochastic Process. Appl. 7 (1) (1978) 9-47. | MR | Zbl
,[25] Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problem biologique, Mosc. Univ. Bull. Math. 1 (1937) 1-25, Translated and reprinted in P. Pelce, Dynamics of Curved Fronts, Academic, San Diego, 1988. | Zbl
, , ,[26] On weighted branching processes in random environment, Stochastic Process. Appl. 109 (1) (2004) 113-144. | MR | Zbl
,[27] Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis, Ann. Inst. H. Poincaré Probab. Statist. 40 (1) (2004) 53-72. | EuDML | Numdam | MR | Zbl
,[28] Martingale convergence and the functional equation in the multi-type branching random walk, Bernoulli 7 (4) (2001) 593-604. | MR | Zbl
, ,[29] Conceptual proofs of criteria for mean behavior of branching processes, Ann. Probab. 23 (3) (1995) 1125-1138. | MR | Zbl
, , ,[30] A simple path to Biggins' martingale convergence for branching random walk, in: , (Eds.), Classical and Modern Branching Processes, Minneapolis, MN, 1994, IMA Vol. Math. Appl., vol. 84, Springer, New York, 1997, pp. 217-221. | MR | Zbl
,[31] Application of Brownian motion to the equation of Kolmogorov-Petrovskiĭ-Piskunov, Comm. Pure Appl. Math. 28 (3) (1975) 323-331. | MR | Zbl
,[32] A correction to: “Application of Brownian motion to the equation of Kolmogorov-Petrovskiĭ-Piskunov” (Comm. Pure Appl. Math. 28 (3) (1975) 323-331), Comm. Pure Appl. Math. 29 (5) (1976) 553-554. | Zbl
,[33] Multiplicative martingales for spatial branching processes, in: Seminar on Stochastic Processes, Princeton, NJ, 1987, Progr. Probab. Statist., vol. 15, Birkhäuser Boston, Boston, MA, 1988, pp. 223-242. | MR | Zbl
,[34] The condition for general branching processes, J. Appl. Probab. 35 (3) (1998) 537-544. | MR | Zbl
,[35] K-P-P-type asymptotics for nonlinear diffusion in a large ball with infinite boundary data and on with infinite initial data outside a large ball, Comm. Partial Differential Equations 20 (7-8) (1995) 1369-1393. | MR | Zbl
,[36] The behavior of solutions of some nonlinear diffusion equations for large time, J. Math. Kyoto Univ. 18 (3) (1978) 453-508. | MR | Zbl
,[37] On the branching process for Brownian particles with an absorbing boundary, J. Math. Kyoto Univ. 4 (1965) 385-398. | MR | Zbl
,Cité par Sources :