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1.
AbstractRealistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries. 相似文献
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Voskresenskaya Olga O. Skorik Nina A. 《Monatshefte für Chemie / Chemical Monthly》2020,151(4):533-542
Monatshefte für Chemie - Chemical Monthly - A comparative analysis is performed on the stability constants $${\upbeta }_{1yn}$$ and intramolecular redox decomposition rate constants $$k_{n\; =... 相似文献
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Olga V. Man’ko 《Acta Physica Hungarica A》2004,19(3-4):313-316
A short review of the general principles of constructing tomograms of spin and quark states is presented. 相似文献
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Andrei Finkelstein Olga Kosheleva Vladik Kreinovich 《International Journal of Theoretical Physics》1997,36(4):1009-1020
Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore,
if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets
that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse
approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized
and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes. 相似文献
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