Abstract
A.B. Vistelius and O.V. Sarmanov drew my attention to a mathematical problem that they were confronted with in the statistical study of bed thickness in geological sediments. The scheme of bed formation considered by them can be understood from the example given in Fig. 1. The horizontal axis represents time, and the vertical axis, the thickness of sediments and washouts. The nth bed is deposited over the time interval (t n-1;s n ) and its thickness (before subsequent washouts) is ξ n = g n —h n1. During time intervals (s n ;t n ) washouts reach the depth n n = g n —h n .
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Dokl. Akad. Nauk SSSR65:6 (1949), 793-796 (in Russian)
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Here we set p < 1. When p = 1, g(x) = 0 for x < 0, f(x) = g(x) and (4) holds trivially.
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© 1992 Springer Science+Business Media Dordrecht
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Shiryayev, A.N. (1992). Solution of A Probabilistic Problem Relating To The Mechanism of Bed Formation. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_37
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DOI: https://doi.org/10.1007/978-94-011-2260-3_37
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