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Low-rank diffusion matrix estimation for high-dimensional time-changed Levy processes
Annales de l'institut Henri Poincare (B) Probability and Statistics. 2018. Vol. 54. No. 3. P. 1583–1621.
Belomestny D., Trabs M.
The estimation of the diffusion matrix Σ of a high-dimensional, possibly time-changed Levy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on Σ. Applying a spectral approach, we construct a weighted least-squares estimator with nuclear-norm-penalisation. We prove oracle inequalities and derive convergence rates for the diffusion matrix estimator. The convergence rates show a surprising dependency on the rank of Σ and are optimal in the minimax sense for fixed dimensions. Theoretical results are illustrated by a simulation study.
Publication based on the results of:
Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43
We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...
Added: June 17, 2026
Nesterov A. S., Журнал Новой экономической ассоциации 2026
В этой статье рассматривается целевой приём в вузы в России с точки зрения науки об устройстве рынков сочетания и экономических механизмов (matching market and mechanism design), ключевого направления современной теории игр. Мы изучаем механизм целевого приёма -- набор правил, по которым устраивается трёхстороннее сочетание между абитуриентом, заказчиком и образовательной программой. Используемый в России механизм имеет ...
Added: June 16, 2026
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 2026
Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162
Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...
Added: June 2, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Petrovanov I., Sergeev A., / Series Computer Science "arxiv.org". 2025. No. 2512.18332.
Transport coding reduces message delay in packet-switched networks by introducing controlled redundancy at the transport layer: original packets are encoded into coded packets, and the message is reconstructed after the first successful deliveries, effectively shifting latency from the maximum packet delay to the -th order statistic. We present a concise, reproducible discrete-event implementation of transport coding in OMNeT++, including ...
Added: December 24, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Chernyshov D., Satanin A., Shchur L., / Series arXiv "math". 2025.
We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K,K(α, τ)) and used to train a convolutional neural network (ResNet18) for binary classification of dynamical regimes. The model reproduces the known critical ...
Added: November 21, 2025
Rubchinskiy A., Chubarova D., / Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2025. No. WP7/2025/01.
The article examines one of the most famous examples of socio-economic systems, characterized by significant uncertainty – the S&P-500 stock market, where shares of 500 largest US companies are traded. No assumptions are made about the probabilistic characteristics of the stock market. A flexible algorithm for daily trading has been developed, based on both known fixed data ...
Added: November 9, 2025
Morozova E., Panov V., Finance Research Letters 2025 Vol. 86 No. A Article 108301
This paper presents a new approach to modeling the Bitcoin prices using the Lévy processes - a class of stochastic processes that are able to realistically capture the jump-type dynamics of financial time series. Our method is inspired by recent research on Bitcoin, which suggests that the prices are closely connected to the media attention ...
Added: September 4, 2025
Morozova E., Panov V., / Series SSRN "ERN: Speculation in Economic Markets". 2025. No. 5222389.
This paper presents a new approach to modeling the Bitcoin prices using the Lévy processes - a class of stochastic processes that are able to realistically capture the jump-type dynamics of financial time series. Our method is inspired by the findings in recent research on Bitcoin, which suggest that the prices are closely connected to ...
Added: May 2, 2025
Morozova E., Panov V., Applied Stochastic Models in Business and Industry 2023 Vol. 39 No. 6 P. 772–788
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Levy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the lowfrequency setup, which ...
Added: June 29, 2023
Morozova E., Panov V., / Series arXiv.org "q-fin.ST". 2022. No. 2210.13824.
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Lévy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the low-frequency setup, which ...
Added: October 26, 2022
Lubashevsky I., Heuer A., Friedrich R. et al., The European Physical Journal B 2010 Vol. 78 P. 207–216
We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148 (2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously ...
Added: November 6, 2021
Lubashevsky I., The European Physical Journal B 2010 Vol. 82 P. 189–195
A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity ...
Added: November 6, 2021