Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes

Fuzzy Sets and Systems

Volumn 160, Issue 21, 2009, Pages 3140-3151

  Aletti, Giacomo ^a   Bongiorno, Enea G ^a   Capasso, Vincenzo ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Birth and growth processes; Fuzzy random sets; Non additive measures; Random closed sets; Set valued processes; Stochastic geometry

Indexed keywords

BIRTH-AND-GROWTH PROCESSES; FUZZY RANDOM SETS; NON-ADDITIVE MEASURES; RANDOM CLOSED SETS; SET-VALUED PROCESSES; STOCHASTIC GEOMETRY;

DOMAIN DECOMPOSITION METHODS; GEOMETRY; MEASUREMENTS; NUCLEATION;

SET THEORY;

EID: 69249223172     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.12.011     Document Type: Article

References (33)

1. G. Aletti, E.G. Bongiorno, V. Capasso, A set-valued framework for birth-and-growth processes, submitted for publication.
2. Aletti G., and Saada D. Survival analysis in Johnson-Mehl tessellation. Statist. Inference Stochastic Process 11 (2008) 55-76
3. Aquilano D., Capasso V., Micheletti A., Patti S., Pizzocchero L., and Rubbo M. A birth and growth model for kinetic-driven crystallization processes, part I: modeling. Nonlinear Anal. Real World Appl. 10 (2009) 71-92
4. Burger M., Capasso V., and Micheletti A. An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes. In: Aletti G., et al. (Ed). Math Everywhere (2007), Springer, Berlin 63-76
5. Burger M., Capasso V., and Pizzocchero L. Mesoscale averaging of nucleation and growth models. Multiscale Model. Simul. 5 (2006) 564-592
6. V. Capasso (Ed.), Mathematical Modelling for Polymer Processing. Polymerization, Crystallization, Manufacturing, Mathematics in Industry, Vol. 2, Springer, Berlin, 2003.
7. Capasso V. On the stochastic geometry of growth. In: Sekimura T., et al. (Ed). Morphogenesis and Pattern Formation in Biological Systems (2003), Springer, Tokyo 45-58
8. Capasso V., and Villa E. Survival functions and contact distribution functions for inhomogeneous, stochastic geometric marked point processes. Stochastic Anal. Appl. 23 (2005) 79-96
9. Chiu S.N. Johnson-Mehl tessellations: asymptotics and inferences. Probability, Finance and Insurance (2004), World Scientific Publishing, River Edge, NJ 136-149
10. Chiu S.N., Molchanov I.S., and Quine M.P. Maximum likelihood estimation for germination-growth processes with application to neurotransmitters data. J. Statist. Comput. Simul. 73 (2003) 725-732
11. Cressie N. Modeling growth with random sets. In: Brunswick M.E. (Ed). Spatial Statistics and Imaging 1988, IMS Lecture Notes Monographs, Series Vol. 20 (1991), Institute of Mathematical Statistics, Hayward, CA 31-45
12. D.J. Daley, D. Vere-Jones, An Introduction to the Theory of Point Processes, Probability and its Applications, second ed., Vol. I, Springer, New York, 2003.
13. Erhardsson T. Refined distributional approximations for the uncovered set in the Johnson-Mehl model. Stochastic Process. Appl. 96 (2001) 243-259
14. Fei W., and Wu R. Doob's decomposition theorem for fuzzy (super) submartingales. Stochastic Anal. Appl. 22 (2004) 627-645
15. Feng Y. Decomposition theorems for fuzzy supermartingales and submartingales. Fuzzy Sets and Systems 116 (2000) 225-235
16. Feng Y., and Zhu X. Semi-order fuzzy supermartingales and submartingales with continuous time. Fuzzy Sets and Systems 130 (2002) 75-86
17. Frost H.J., and Thompson C.V. The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures. Acta Metall. 35 (1987) 529-540
18. Herrick J., Jun S., Bechhoefer J., and Bensimon A. Kinetic model of DNA replication in eukaryotic organisms. J. Mol. Biol. 320 (2002) 741-750
19. Keimel K., and Roth W. Ordered Cones and Approximation, Lecture Notes in Mathematics Vol. 1517 (1992), Springer, Berlin
20. Li S., Ogura Y., and Kreinovich V. Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (2002), Kluwer Academic Publishers Group, Dordrecht
21. Matheron G. Random Sets and Integral Geometry (1975), Wiley, New York, London, Sydney
22. A. Micheletti, S. Patti, E. Villa, Crystal growth simulations: a new mathematical model based on the Minkowski sum of sets, in: D. Aquilano, et al., (Eds.), Industry Days 2003-2004, The MIRIAM Project, Vol. 2, Esculapio, Bologna, 2005, pp. 130-140.
23. Molchanov I.S. Limit theorems for unions of random closed sets. Lecture Notes in Mathematics Vol. 1561 (1993), Springer, Berlin
24. Molchanov I.S. Statistics of the Boolean Model for Practitioners and Mathematicians (1997), Wiley, Chichester
25. Molchanov I.S., and Chiu S.N. Smoothing techniques and estimation methods for nonstationary Boolean models with applications to coverage processes. Biometrika 87 (2000) 265-283
26. Møller J. Random Johnson-Mehl tessellations. Adv. Appl. Probab. 24 (1992) 814-844
27. Møller J. Generation of Johnson-Mehl crystals and comparative analysis of models for random nucleation. Adv. Appl. Probab. 27 (1995) 367-383
28. Møller J., and Sørensen M. Statistical analysis of a spatial birth-and-death process model with a view to modelling linear dune fields. Scand. J. Statist. 21 (1994) 1-19
29. Nguyen H.T. An Introduction to Random Sets (2006), Chapman & Hall/CRC, Boca Raton, FL
30. Rådström H. An embedding theorem for spaces of convex sets. Proc. Amer. Math. Soc. 3 (1952) 165-169
31. Serra J. Image Analysis and Mathematical Morphology (1984), Academic Press Inc., Harcourt Brace Jovanovich Publishers, London
32. Stoyan D., Kendall W.S., and Mecke J. Stochastic Geometry and its Applications. second ed. (1995), Wiley, Chichester
33. Terán P. Cones and decomposition of sub- and supermartingales. Fuzzy Sets and Systems 147 (2004) 465-474