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On Some Qualitative Properties of the Boolean Model of Stochastic Geometry
Author(s) -
Stoyan Dietrich
Publication year - 1979
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19790590907
Subject(s) - boolean model , monotonic function , mathematics , stochastic geometry , relation (database) , function (biology) , boolean function , covariance , characterization (materials science) , pure mathematics , discrete mathematics , computer science , mathematical analysis , statistics , biology , nanotechnology , database , materials science , evolutionary biology
For the Boolean model, one of the basic models of stochastic geometry and stereology, monotonicity and continuity properties are proved. In particular, for Boolean models on the line the relation between primary and number granulometry is discussed, and monotonicity properties of the covariance function are studied. Finally, the probability of hitting of an arbitrary primary grain by one of the other ones is considered.