Free Access
Issue
ESAIM: PS
Volume 15, 2011
Page(s) 402 - 416
DOI https://doi.org/10.1051/ps/2010009
Published online 05 January 2012
  1. G. Aletti, E.G. Bongiorno and V. Capasso, Statistical aspects of fuzzy monotone set-valued stochastic processes. application to birth-and-growth processes. Fuzzy Set. Syst. 160 (2009) 3140–3151. [Google Scholar]
  2. G. Aletti and D. Saada, Survival analysis in Johnson-Mehl tessellation. Stat. Infer. Stoch. Process. 11 (2008) 55–76. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Aquilano, V. Capasso, A. Micheletti, S. Patti, L. Pizzocchero and M. Rubbo, A birth and growth model for kinetic-driven crystallization processes, part i: Modeling. Nonlinear Anal. Real World Appl. 10 (2009) 71–92. [CrossRef] [Google Scholar]
  4. J. Aubin and H. Frankowska, Set-valued Analysis. Birkhäuser, Boston Inc. (1990). [Google Scholar]
  5. G. Barles, H.M. Soner and P.E. Souganidiss, Front propagation and phase field theory. SIAM J. Control Optim. 31 (1993) 439–469. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Burger, Growth fronts of first-order Hamilton-Jacobi equations. SFB Report 02-8, University Linz, Linz, Austria (2002). [Google Scholar]
  7. M. Burger, V. Capasso and A. Micheletti, An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes, in Math Everywhere. G. Aletti et al. Eds., Springer, Berlin (2007) 63–76. [Google Scholar]
  8. M. Burger, V. Capasso and L. Pizzocchero, Mesoscale averaging of nucleation and growth models. Multiscale Model. Simul. 5 (2006) 564–592 (electronic). [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. V. Capasso (Ed.) Mathematical Modelling for Polymer Processing. Polymerization, Crystallization, Manufacturing. Mathematics in Industry 2, Springer-Verlag, Berlin (2003). [Google Scholar]
  10. V. Capasso, On the stochastic geometry of growth, in Morphogenesis and Pattern Formation in Biological Systems. T. Sekimura, et al. Eds., Springer, Tokyo (2003) 45–58. [Google Scholar]
  11. V. Capasso and D. Bakstein, An Introduction to Continuous-Time Stochastic Processes. Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston Inc. (2005). [Google Scholar]
  12. V. Capasso and E. Villa, Survival functions and contact distribution functions for inhomogeneous, stochastic geometric marked point processes. Stoch. Anal. Appl. 23 (2005) 79–96. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions. Lecture Notes Math. 580, Springer-Verlag, Berlin (1977). [Google Scholar]
  14. S.N. Chiu, Johnson-Mehl tessellations: asymptotics and inferences, in Probability, finance and insurance. World Sci. Publ., River Edge, NJ (2004) 136–149. [Google Scholar]
  15. S.N. Chiu, I.S. Molchanov and M.P. Quine, Maximum likelihood estimation for germination-growth processes with application to neurotransmitters data. J. Stat. Comput. Simul. 73 (2003) 725–732. [CrossRef] [Google Scholar]
  16. N. Cressie, Modeling growth with random sets. In Spatial Statistics and Imaging (Brunswick, ME, 1988). IMS Lecture Notes Monogr. Ser. 20, Inst. Math. Statist., Hayward, CA (1991) 31–45. [Google Scholar]
  17. D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes. Probability and its Applications, I, 2nd edition, Springer-Verlag, New York (2003). [Google Scholar]
  18. N. Dunford and J.T. Schwartz, Linear Operators. Part I. Wiley Classics Library, John Wiley & Sons Inc., New York (1988). [Google Scholar]
  19. T. Erhardsson, Refined distributional approximations for the uncovered set in the Johnson-Mehl model. Stoch. Proc. Appl. 96 (2001) 243–259. [CrossRef] [Google Scholar]
  20. H.J. Frost and C.V. Thompson, The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures. Acta Metallurgica 35 (1987) 529–540. [CrossRef] [Google Scholar]
  21. E. Giné, M.G. Hahn and J. Zinn, Limit theorems for random sets: an application of probability in Banach space results. In Probability in Banach Spaces, IV (Oberwolfach, 1982). Lecture Notes Math. 990, Springer, Berlin (1983) 112–135. [Google Scholar]
  22. J. Herrick, S. Jun, J. Bechhoefer and A. Bensimon, Kinetic model of DNA replication in eukaryotic organisms. J. Mol. Biol. 320 (2002) 741–750. [CrossRef] [PubMed] [Google Scholar]
  23. F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions. J. Multivariate Anal. 7 (1977) 149–182. [CrossRef] [MathSciNet] [Google Scholar]
  24. C.J. Himmelberg, Measurable relations. Fund. Math. 87 (1975) 53–72. [MathSciNet] [Google Scholar]
  25. S. Li, Y. Ogura and V. Kreinovich, Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Kluwer Academic Publishers Group, Dordrecht (2002). [Google Scholar]
  26. G. Matheron, Random Sets and Integral Geometry, John Wiley & Sons, New York-London-Sydney (1975). [Google Scholar]
  27. A. Micheletti, S. Patti and E. Villa, Crystal growth simulations: a new mathematical model based on the Minkowski sum of sets, in Industry Days 2003-2004 The MIRIAM Project 2, D. Aquilano et al. Eds., Esculapio, Bologna (2005) 130–140. [Google Scholar]
  28. I.S. Molchanov, Statistics of the Boolean Model for Practitioners and Mathematicians. Wiley, Chichester (1997). [Google Scholar]
  29. I.S. Molchanov and S.N. Chiu, Smoothing techniques and estimation methods for nonstationary Boolean models with applications to coverage processes. Biometrika 87 (2000) 265–283. [CrossRef] [Google Scholar]
  30. J. Møller, Random Johnson-Mehl tessellations. Adv. Appl. Prob. 24 (1992) 814–844. [CrossRef] [Google Scholar]
  31. J. Møller, Generation of Johnson-Mehl crystals and comparative analysis of models for random nucleation. Adv. Appl. Prob. 27 (1995) 367–383. [CrossRef] [Google Scholar]
  32. J. Møller and M. Sørensen, Statistical analysis of a spatial birth-and-death process model with a view to modelling linear dune fields. Scand. J. Stat. 21 (1994) 1–19. [Google Scholar]
  33. H. Rådström, An embedding theorem for spaces of convex sets. Proc. Am. Math. Soc. 3 (1952) 165–169. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Serra, Image Analysis and Mathematical Morphology. Academic Press Inc., London (1984). [Google Scholar]
  35. L. Shoumei and R. Aihong, Representation theorems, set-valued and fuzzy set-valued Ito integral. Fuzzy Set. Syst. 158 (2007) 949–962. [CrossRef] [Google Scholar]
  36. D. Stoyan, W.S. Kendall and J. Mecke, Stochastic Geometry and its Applications. 2nd edition, John Wiley & Sons Ltd., Chichester (1995). [Google Scholar]

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