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841.
A. Baltrünas 《Lithuanian Mathematical Journal》1999,39(3):240-244
The Sparre Andersen model in the collective risk theory is investigated. We obtain the rate of convergence for the ruin probability
after thenth payoff in the case where claim sizes are heavy tailed (say, subexponential).
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys,
Vol. 39, No. 3, pp. 304–309, July–September, 1999. 相似文献
842.
Vilius Stakénas 《Lithuanian Mathematical Journal》1999,39(1):86-101
This paper is concerned with the sieve problem for Farey fractions (i.e., rational numbers with denominators less thanx) lying in an interval (λ1, λ2). An asymptotic formula for the sifting function is derived under the assumption that (λ1, λ2)x→∞ asx→∞. Two applications of this result are made. In the first one, the value distribution of the vector η(m/n)=(ξ(m), ξ(n)) is considered; here, fork=p
1
p
2...p
s
,p
1≥p
2>-..., ξk)_is defined by ξ(k)=(logp
1/logk, logp
2/logk,..., logp
s
/logk, 0, ...); allp
i
are prime numbers. It is shown that the limit distribution is π×π, where π is the Poisson-Dirichlet distribution. The asymptotical
behavior of finite-dimensional distributions of ξ(k) for natural numbers was studied by Billingsley, Knuth, Trabb Pardo, Vershik, and others; the result of weak convergence
to the Poisson-Dirichlet distribution appears in Donnelly and Grimmett. The second application is concerned with the density
of sets {m/n: f(m/n)=a}, wheref is a function with the almost squareful kernel.
Supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2600, Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1,
pp. 108–127, January–March, 1999.
Translated by V. Stakénas 相似文献
843.
Rytis Juršėnas 《Mathematische Nachrichten》2023,296(8):3411-3448
Let be an isometric boundary pair associated with a closed symmetric linear relation T in a Krein space . Let be the Weyl family corresponding to . We cope with two main topics. First, since need not be (generalized) Nevanlinna, the characterization of the closure and the adjoint of a linear relation , for some , becomes a nontrivial task. Regarding as the (Shmul'yan) transform of induced by Γ, we give conditions for the equality in to hold and we compute the adjoint . As an application, we ask when the resolvent set of the main transform associated with a unitary boundary pair for is nonempty. Based on the criterion for the closeness of , we give a sufficient condition for the answer. From this result it follows, for example, that, if T is a standard linear relation in a Pontryagin space, then the Weyl family corresponding to a boundary relation Γ for is a generalized Nevanlinna family; a similar conclusion is already known if T is an operator. In the second topic, we characterize the transformed boundary pair with its Weyl family . The transformation scheme is either or with suitable linear relations V. Results in this direction include but are not limited to: a 1-1 correspondence between and ; the formula for , for an ordinary boundary triple and a standard unitary operator V (first scheme); construction of a quasi boundary triple from an isometric boundary triple with and (second scheme, Hilbert space case). 相似文献
844.
845.
Survila Arvydas Kanapeckaitė Stasė Staišiūnas Laurynas 《Journal of Solid State Electrochemistry》2023,27(7):1813-1820
Journal of Solid State Electrochemistry - The anodic behavior of the alkaline Cu | Cu(II), glycine system was investigated by RDE voltammetry combined with EQCM measurements. Well-defined current... 相似文献