C. Mueller, und R. Sowers. Stochastic analysis (Ithaca, NY, 1993), Volume 57 von Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, Finally, T. Shiga has pointed out that there is a dual process for (1.4),
which is a system of branching Brownian motions, in which particles
coalesce at a Poisson rate, measured according to the local time beween
pairs of particles. We do not give a more precise description..(1995)
A. Kolmogorov. Izv. Akad. Nauk SSSR, Ser. Math, (1937)Computes density of fairly general Johnson-Mehl crystals and the probability that a point is not in a crystal yet..
D. Mollison. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Seite 579--614. Berkeley, Calif., Univ. California Press, (1972)
M. Bramson, R. Durrett, und G. Swindle. Ann. Probab., 17 (2):
444--481(1989)This paper examines a version of the contact process with a large range. Particles die at rate 1, and a particle is created at an empty site $x$ at rate $łambda$ times the fraction of occupied sites in $y:||x-y||M$. This contact process is dominated by a branching random walk with death rate 1 and birth rate $łambda$, and it is shown that in many ways these two processes are very similar when $M$ is large. In particular, as $M\toınfty$, the critical value for the contact process converges to 1, which is the critical value for branching random walks. The authors obtain precise rates for this convergence, in every dimension, enabling them to describe the ``crossover'' from contact process to branching process behavior in terms of the survival probability of a process started from a single particle. The proofs of the main results use many estimates for branching random walks, further detailing the nature of this crossover behavior..
A. Volpert, V. Volpert, und V. Volpert. Translations of Mathematical Monographs American Mathematical Society, Providence, RI, (1994)Translated from the Russian manuscript by James F. Heyda.
J. Biggins. (2010)cite arxiv:1003.4715
Comment: To appear in: Probability and Mathematical Genetics: Papers in Honour
of Sir John Kingman, Cambridge University Press, 2010, 112-133.
D. Aronson, und H. Weinberger. Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974), Lecture Notes in Math., Vol. 446, Springer, Berlin, (1975)
A. Kolmogorov, I. Petrovskii, und N. Piscunov. Selected Works of A.N. Kolmogorov: Mathematics and mechanics, Volume 25 von Mathematics and its Applications (Soviet Series), Springer Netherlands, (1991)