Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biggins, J. (1992) Uniform convergence in the branching random walk, Ann. Probab., 20, 137–151
Breiman, L. (1968) Probability. Addison-Wesley, London.
Champneys, A, Harris, S. C., Toland, J. F., Warren, J. & Williams, D (1995) Analysis, algebra and probability for a coupled system of reaction-diffusion equations, Phil. Trans. Roy. Soc. London (A), 350, 69–112.
Chauvin, B. & Rouault, A. (1997) Boltzmann-Gibbs weights in the branching random walk. Classical and Modern Branching Processes (ed. Athreya, Krishna, et al.), IMA Vol. Math. Appl., 84, pp 41–50. Springer, New York.
Git, Y. & Harris, S.C. (2000) Large-deviations and martingales for a typed branching diffusion: II, (In preparation).
Harris, S.C. & Williams, D. (1996) Large-deviations and martingales for a typed branching diffusion: I, Astérisque, 236, 133–154.
Harris, S.C. (2000) A typed branching diffusion, a reaction-diffusion equation and travelling-waves. (In preparation).
McKean, H. P. (1975) Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math. 28, 323–331.
McKean, H. P. (1976) Correction to the above. Comm. Pure Appl. Math. 29, 553–554.
Neveu, J. (1987) Multiplicative martingales for spatial branching processes. Seminar on Stochastic Processes (ed. E. Çinlar, K. Chung and R. Getoor), Progress in Probability & Statistics. 15. pp. 223–241. Birkhäuser, Boston.
Revuz, D. & Yor, M. (1991) Continuous martingales and Brownian motion. Springer, Berlin.
Rogers, L.C.G. & Williams, D. (1994) Diffusions, Markov processes and martingales. Volume 1: Foundations. (Second Edition). Wiley, Chichester and New York.
Rogers, L.C.G. & Williams, D. (1987) Diffusions, Markov processes and martingales. Volume 2: Itô Calculus. Wiley, Chichester and New York.
Szegö, G. (1967) Orthogonal Polynomials (Third Edition). American Mathematical Society Colloquium Publications, Volume XXIII.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2000 Springer-Verlag
About this chapter
Cite this chapter
Harris, S.C. (2000). Convergence of a ‘gibbs-boltzmann’ random measure for a typed branching diffusion. In: Azéma, J., Ledoux, M., Émery, M., Yor, M. (eds) Séminaire de Probabilités XXXIV. Lecture Notes in Mathematics, vol 1729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103806
Download citation
DOI: https://doi.org/10.1007/BFb0103806
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67314-9
Online ISBN: 978-3-540-46413-6
eBook Packages: Springer Book Archive