Stochastic representations of max-type functionals of a random walk

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Stochastic representations of max-type functionals of a random walk

Theory of Probability and Its Applications. 2010. Vol. 54. No. 3. P. 516–525.

In this paper we consider the problems of finding stochastic representations of functional F = F(ω) of a random walk. We obtain both single and multiple representations of functionals FN = max k ≦ N Sk, Fτ-a = max k ≦ τ-a Sk, where τ-a is the time of the first reaching the level-a, a ∈ N, by a random walk. Also we obtain a single representation of functional FgN = maxk ≦ gN S k, where gN is the time of the last zero of a random walk on (0, N]

Research target: Mathematics

Language: English

DOI

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An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...

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Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...

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М.: Юрайт, 2026.

The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...

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The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...

Added: October 9, 2026

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Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124

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Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184

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Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.

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Lyulko Y., Theory of Probability and Its Applications 2012 Vol. 56 No. 1 P. 140–149

Added: August 28, 2024

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Karpov I., Glazkova E., , in: Recent Trends in Analysis of Images, Social Networks and Texts. 9th International Conference, AIST 2020, Skolkovo, Moscow, Russia, October 15–16, 2020 Revised Supplementary ProceedingsVol. 12602.: Springer, 2021. P. 11–21.

The widespread of Online Social Networks and the opportunity to commercialize popular accounts have attracted a large number of automated programs, known as artificial accounts. This paper (Project repository available at http://github.com/karpovilia/botdetection) focuses on the classification of human and fake accounts on the social network, by employing several graph neural networks, to efficiently encode attributes and ...

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Konakov V., Menozzi S., Molchanov S., , in: Contemporary MathematicsVol. 739: Probabilistic Methods in Geometry, Topology and Spectral Theory.: AMS, 2019. P. 97–124.

This paper is concerned with Random walk approximations of the Brownian motion on the Affine group Aff(R). We are in particular interested in the case where the innovations are discrete. In this framework, the return probabilities of the walk have fractional exponential decay in large time, as opposed to the polynomial one of the continuous object. We prove that ...

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Molchanov S., Vainberg B., SIAM Journal on Mathematical Analysis 2019 Vol. 51 No. 3 P. 1824–1835

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V.L. Kreps, Automation and Remote Control 2019 Vol. 80 No. 2 P. 362–379

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