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Relevant bibliographies by topics / Kolmogorov continuity theorem

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Journal articles

Academic literature on the topic 'Kolmogorov continuity theorem'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Kolmogorov continuity theorem"

1

Kharkevich, Yuri I., and Alexander G. Khanin. "APPROXIMATIVE PROPERTIES OF ABEL–POISSON-TYPE OPERATORS ON THE GENERALIZED HÖLDER CLASSES." Journal of Automation and Information sciences 1 (January 1, 2021): 76–83. http://dx.doi.org/10.34229/0572-2691-2021-1-6.

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The paper deals with topical issues of the modern applied mathematics, in particular, an investigation of approximative properties of Abel–Poisson-type operators on the so-called generalized Hölder’s function classes. It is known, that by the generalized Hölder’s function classes we mean the classes of continuous -periodic functions determined by a first-order modulus of continuity. The notion of the modulus of continuity, in turn, was formulated in the papers of famous French mathematician Lebesgue in the beginning of the last century, and since then it belongs to the most important character

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2

Fundator, Michael. "APPLICATION OF MULTIDIMENSIONAL TIME MODEL TO DYNAMICAL RELATION OF POISSON SPIKE TRAINS IN NEURAL ION CURRENT MODELS AND FORMATION OF NON-CANONICAL BASES, ISLANDS, AND G-QUADRUPLEXES IN DNA, MRNA, AND RNA AT OR NEAR THE TRANSCRIPTION." International Journal of Research -GRANTHAALAYAH 9, no. 1 (2021): 7–15. http://dx.doi.org/10.29121/granthaalayah.v9.i1.2021.2918.

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Ground breaking application of mathematics and biochemistry to explain formation of non-canonical bases, islands, G-quadruplex structures, and analog bases in DNA and mRNA at or near the transcription with connection to neural networks is implemented using statistical and stochastic methods apparatus with the addition of quantum principles. As a result the usual transience of Poisson spike trains (PST) becomes very instrumental tool for finding periodical type of solutions to Fokker-Plank (FP) stochastic differential equation (SDE). The present study develops new multidimensional methods of fi

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3

Rozora, I. V. "Analytical properties of sample paths of some stochastic processes." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2020): 11–15. http://dx.doi.org/10.17721/1812-5409.2020/4.1.

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The study of the analytical properties of random processes and their functionals, without a doubt, was and remains the relevant topic of the theory of random processes. The first result from which the study of the local properties of random processes began is Kolmogorov’s theorem on sample continuity with probability one. The classic result for Gaussian random processes is Dudley’s theorem. This paper is devoted to the study of local properties of sample paths of random processes that can be represented as a sum of squares of Gaussian random processes. Such processes are called square-Gaussian

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4

GRAHOVAC, DANIJEL, and NIKOLAI N. LEONENKO. "BOUNDS ON THE SUPPORT OF THE MULTIFRACTAL SPECTRUM OF STOCHASTIC PROCESSES." Fractals 26, no. 04 (2018): 1850055. http://dx.doi.org/10.1142/s0218348x1850055x.

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The multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper, we establish bounds on the support of the spectrum of singularities. To do this, we prove a theorem that complements the famous Kolmogorov’s continuity criterion. The nature of these bounds helps us to identify the quantities truly responsible for the support of the spectrum. We then make several conclusions from this. First, specifying global scaling in terms of

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5

Nakajima, Shohei. "Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients." Stochastics and Partial Differential Equations: Analysis and Computations, June 9, 2021. http://dx.doi.org/10.1007/s40072-021-00199-6.

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AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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6

"Transition functions, paths and path integrals." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 434, no. 1890 (1991): 41–63. http://dx.doi.org/10.1098/rspa.1991.0079.

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The main theme of this expository paper is the relation between analysis and probability in the context of diffusion theory. Section 1 discusses in rather heuristic fashion the very satisfying solution to the problem of describing diffusion processes which Kolmogorov achieved via PDE theory (the theory of partial differential equations) and his criterion for path continuity. Section 2 describes how Itô calculus totally transformed the subject by allowing us to construct the sample paths of a diffusion process X by solving an SDE (stochastic differential equation) driven by brownian motion. (Of

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