On the generalized geometric densities of random closed sets. An application to growth processes

Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry. Dedicated to the 60th Birthday of Vincenzo Capasso

Volumn , Issue , 2007, Pages 77-91

  Capasso, Vincenzo ^a   Villa, Elena ^a  

^a UNIVERSITY OF MILAN   (Italy)

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EID: 84892197089     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-44446-6_7     Document Type: Chapter

References (26)

1. Ambrosio, L., Capasso, V., Villa, E.: On the approximation of geometric densities of random closed sets. RICAM Report 14/2006, Linz. Available at: http://www.ricam.oeaw.ac.at/publications/reports.
2. Ambrosio, L., Colesanti, A., Villa, E.: First order Steiner formulas for some classes of closed sets. An application to stochastic geometry. In preparation.
3. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Press, Oxford, (2000).
4. Araujo, A., Giné, E.: The Central Limit Theorem for Real and Banach Valued Random Variables. John Wiley & Sons, New York, (1980).
5. Baddeley, A.J., Molchanov, I.S.: On the expected measure of a random set. In: Proceedings of the International Symposium on Advances in Theory and Applications of Random Sets (Fontainebleau, 1996). World Sci. Publishing, River Edge, NJ, 3-20, (1997).
6. Barles, G., Soner, H.M., Souganidis, P.E.: Front propagation and phase-field theory. SIAM J. Contr.Optim., 31, 439-469 (1993).
7. Bosq, D.: Linear Processes in Function Spaces. Theory and Applications. Lecture Notes in Statistics 149, Springer-Verlag, New York, (2000).
8. Burger, M.: Growth fronts of first-order Hamilton-Jacobi equations. SFB Report 02-8, J. Kepler University, Linz (2002).
9. Burger, M., Capasso, V., Salani, C.: Modelling multi-dimensional crystallization of polymers in interaction with heat transfer. Nonlinear Analysis: Real World Application, 3, 139-160 (2002).
10. Mathematical Modelling for Polymer Processing Polymerization, Crystallization, Manufacturing (V. Capasso, Editor) Mathematics in Industry Vol 2, Springer Verlag, Heidelberg (2003).
11. Capasso, V., Micheletti, A.: Stochastic geometry and related statistical problems in biomedicine. In: Complex Systems in Biomedicine (Quarteroni, A. et al., Eds.) Springer, Milano (2006).
12. Capasso, V., Villa, E.: Survival functions and contact distribution functions for inhomogeneous, stochastic geometric marked point processes. Stoch. An. Appl., 23, 79-96 (2005).
13. Capasso, V., Villa, E.: On the geometric densities of random closed sets. RICAM Report 13/2006, Linz. Available at: http://www.ricam.oeaw.ac.at/ publications/reports.
14. Falconer, K.J.: The Geometry of Fractal Sets. Cambridge University press, Cambridge, (1985).
15. Federer, H.: Curvature Measures, Trans. Amer. Math. Soc., 93, 418-491 (1959).
16. Gelfand I.M., Shilov G.E.: Generalized Functions. Properties and operations. Academic Press, New York, (1964).
17. Hug, D., Last, G., Weil, W.: A local Steiner-type formula for general closed sets and applications. Math. Z. 246, no. 1-2, 237-272 (2004).
18. Kiderlen, M., Rataj, J.: On infinitesimal increase of volumes of morphological transforms. Thiele Research Report 14/2005, Aarhus. Available at: http://www.imf.au.dk/cgi-bin/dlf/viewpublications.cgi?id=580.
19. Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Prentice-Hall, Englewood Cliffs (N.J.), (1970).
20. Last, G., Brandt, A.: Marked Point Processes on the Real Line. The Dynamic Approach. Springer, New York (1995).
21. Matheron, G.: Les Variables Regionaliśees et leur Estimation, Masson et Cie, Paris, (1965).
22. Matheron, G.: Random Sets and Integral Geometry. John Wiley & Sons, New York, (1975).
23. Rataj, J.: On boundaries of unions of sets with positive reach. Beiträge Algebra Geom. 46, 397-404 (2005).
24. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London, (1984).
25. Villa, E.: Methods of Geometric Measure Theory in Stochastic Geometry. PhD thesis, University of Milan, Milan (2006).
26. Zähle M.; Random processes of Hausdorff rectifiable closed sets. Math. Nachr., 108, 49-72 (1982).