Johnson-Mehl tessellations: asymptotics and inferences

Research output: Chapter in book/report/conference proceedingChapterpeer-review


Seeds are randomly scattered in ℝd according to a spatial-temporal point process. Each seed has its own potential germination time. Each seed that succeeds in germinating will be the centre of a growing spherical inhibited region that prohibits germination of any seed with later potential germination time. The radius of an inhibited region at time t after the germination of the seed at its centre is vt. The set of locations first reached by the growth of the inhibited region originated from x is called the cell of x. The space will be partitioned into cells and this space-filling structure is called the Johnson–Mehl tessellation. We show that the time until a large cube is totally inhibited has an extreme value distribution. In particular, for d = 1, we obtain the exact distribution of this time by transforming the original process to a Markov process. Moreover, we prove a central limit theorem for the number of germinations within [0, L)d. Finally, the maximum likelihood estimation for v, a nonparametric estimation for the intensity measure and for its density, and the maximum likelihood estimation for the parameters of the intensity with known analytical form are proposed.
Original languageEnglish
Title of host publicationProbability, Finance and Insurance
EditorsTze Leung Lai, Hailiang Yang , Siu Pang Yung
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages14
ISBN (Electronic)9789814482615, 9789812702715
ISBN (Print)9789812388537
Publication statusPublished - Jun 2004
EventWorkshop on Probability, Finance and Insurance - The University of Hong Kong, Hong Kong
Duration: 15 Jul 200217 Jul 2002


WorkshopWorkshop on Probability, Finance and Insurance
Country/TerritoryHong Kong


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