Expectation and variance of the volume covered by a large number of independent random sets
Compositio Mathematica, Tome 52 (1984) no. 1, pp. 57-83.
@article{CM_1984__52_1_57_0,
     author = {Stam, A. J.},
     title = {Expectation and variance of the volume covered by a large number of independent random sets},
     journal = {Compositio Mathematica},
     pages = {57--83},
     publisher = {Martinus Nijhoff Publishers},
     volume = {52},
     number = {1},
     year = {1984},
     mrnumber = {742698},
     zbl = {0546.60015},
     language = {en},
     url = {http://www.numdam.org/item/CM_1984__52_1_57_0/}
}
TY  - JOUR
AU  - Stam, A. J.
TI  - Expectation and variance of the volume covered by a large number of independent random sets
JO  - Compositio Mathematica
PY  - 1984
SP  - 57
EP  - 83
VL  - 52
IS  - 1
PB  - Martinus Nijhoff Publishers
UR  - http://www.numdam.org/item/CM_1984__52_1_57_0/
LA  - en
ID  - CM_1984__52_1_57_0
ER  - 
%0 Journal Article
%A Stam, A. J.
%T Expectation and variance of the volume covered by a large number of independent random sets
%J Compositio Mathematica
%D 1984
%P 57-83
%V 52
%N 1
%I Martinus Nijhoff Publishers
%U http://www.numdam.org/item/CM_1984__52_1_57_0/
%G en
%F CM_1984__52_1_57_0
Stam, A. J. Expectation and variance of the volume covered by a large number of independent random sets. Compositio Mathematica, Tome 52 (1984) no. 1, pp. 57-83. http://www.numdam.org/item/CM_1984__52_1_57_0/

[1] L. De Haan: On regular variation and its application to the weak convergence of sample extremes. Mathematical Centre Tracts 32. Amsterdam: Mathematisch Centrum, 1970. | MR | Zbl

[2] M.P. D: Differential Geometry of Curves and Surfaces. Englewood Cliffs, New Jersey: Prentice Hall, 1976. | MR | Zbl

[3] W. Feller: An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. New York: Wiley, 1971. | MR | Zbl

[4] W. Gröbner and N. Hofreiter: Integral-Tafel, Zweiter Teil: bestimmte Integrale. Wien 1950.

[5] H. Hadwiger: Altes und Neues über konvexe Körper. Basel und Stuttgart: Birkhäuser Verlag, 1955. | MR | Zbl

[6] P.A.P. Moran: The volume occupied by normally distributed spheres. Acta Math. 133 (1974) 273-286. | MR | Zbl

[7] E. Seneta: Regularly Varying Functions.Lecture Notes in Mathematics 508. Berlin: Springer Verlag, 1976. | MR | Zbl

[8] A.J. Stam: The variance of the volume covered by a large number of rectangles with normally distributed centers. Report T. W. 218, Mathematisch Instituut Rijksuniversiteit Groningen.

[9] A.J. Stam: The volume covered by a large number of random sets: examples. Report T. W.-245, Mathematisch Instituut Rijksuniversiteit, Groningen.

[10] F.A. Valentine: Konvexe Mengen. Mannheim: Bibliographisches Institut, 1968. | MR | Zbl