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.
D. Daley, und D. Vere-Jones. Stochastic point processes: statistical analysis, theory, and applications (Conf., IBM Res. Center, Yorktown Heights, N.Y., 1971), Wiley-Interscience, New York, (1972)
D. Daley, und D. Vere-Jones. Probability and its Applications (New York) Springer-Verlag, New York, Second Edition, (2003)Elementary theory and methods.
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..
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)
N. Berestycki. Ensaios Matematicos, 16, cite arxiv:0909.3985
Comment: Lecture notes, to appaear in the collection "Ensaios Matematicos". 17
figures.(2009)
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..