Vorobyev, Oleg Yu.
(2013):
*In search of a primary source: remaking the paper (1975) where at the first time a definition of lattice (Vorob’ev) expectation of a random set was given.*
Published in: XII International Conference on FAM and Eventology of Safety, Siberian Federal University, Krasnoyarsk, Russia, 2013
(27 April 2013): pp. 32-38.

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## Abstract

Remaking the primary source of an old good idea of the “lattice expectation”, published by me in 1975 at the first time and subsequently, especially in the western literature on stochastic geometry and the theory of random sets, named from a light hand of Dietrich Stoyan [1994] “Vorob’ev expectation”; had an only historical and methodic value for eventology and probability theory once more reminding how and “...from what rubbish flowers grow, not knowing shame”.

Item Type: | MPRA Paper |
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Original Title: | In search of a primary source: remaking the paper (1975) where at the first time a definition of lattice (Vorob’ev) expectation of a random set was given |

English Title: | In search of a primary source: remaking the paper (1975) where at the first time a definition of lattice (Vorob’ev) expectation of a random set was given |

Language: | English |

Keywords: | Probability theory, random set, mean measure set, lattice expectation, Vorob’ev expectation, eventology. |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General |

Item ID: | 48102 |

Depositing User: | Prof Oleg Yu Vorobyev |

Date Deposited: | 08 Jul 2013 07:22 |

Last Modified: | 01 Oct 2019 05:58 |

References: | [2] O. Yu. Vorobyev. Definition of probabilities of fire spread and estimating mean forest fire spread sets. The Guarding of Siberia Forest Resources. Krasnoyarsk, The Sukachev Institute of Forest and Wood, USSR AS, SB, 1:43–67, 1975 (in Russian), URL: http://eventology-theory.com/0- lec/remake-1975-full-GSFR-43-67.pdf. [3] D Stoyan and H. Stoyan. Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. XIV. John Wiley & Sons, Chichester etc., 1994, 389p. [5] O. Yu. Vorobyev. Mathematical description of random spread processes and its control. Izvestia of SB AS USSR, 13(3):146–152, 1973 (in Russian). [7] O. Yu. Vorobyev. Mean Measure Modeling. Nauka, Moscow, 1984 (in Russian). [9] Probability and Mathematical Statistics. Encyclopedia. Science publisher Great Russian Encyclopedia, Moscow, 1999 (in Russian). [10] P. Heinrich, R. C. Stoica, and V. C. Tran. Level sets esimation and Vorob’ev expectation of random compact sets. Spatial Statistics, 2:47–61, December 2012. [11] C. Chevalier, D. Ginsbourger, J. Bect, and Molchanov I. Estimating and Quantifying Uncertainties on Level Sets Using the Vorob’ev Expectation and Deviation with Gaussian Process Models. Contributions to Statistics. Advances in Model-Oriented Design and Analysis � mODa 10. D. Uci´n ski et al. (eds.), pages 35–43. Springer International Publishing, Switzerland, 2013. [12] I. Molchanov. Theory of Random Sets. Springer-Verlag, London etc., 2005. [14] O. Yu. Vorobyev. On set characterictics of states of distributed probability prosesses. Izvestia of SB AS USSR, 3(3):3–7, 1977 (in Russian). [16] S. Kovyazin. On the limit behavior of a class of empirical means of a random set. Theory of Probability and its Applications, 30(4):814–820. Translated from Russian by J. Malek., 1986. [18] O. Yu. Vorobyev. Eventology. Siberian Federal University, Krasnoyarsk, Russia, 2007, 435p. (in Russian, abstract in English), http://eventology-theory.com/0-books/1- VorobyevOleg�2007�Eventology�435p.pdf. [20] O. Yu. Vorobyev. A mean probability event for a set of events. In. Proc. of the XI Intern. FAMES Conf. on Financial and Actuarial Mathematics and Eventology of Safety, Krasnoyarsk, SFU (Oleg Vorobyev ed.):139–147, 2012 (in Russian, abstract in English). |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/48102 |