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A class of multifractal processes constructed using an embedded branching process
The Annals of Applied Probability. 2012. Vol. 22. No. 6. P. 2357-2387.
Decrouez G. G., Jones O. D.
In press
We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+1 in O(log n) operations. Detailed pseudo-code for this algorithm is provided.R
Decrouez G. G., Hambly B., Jones O. D., Stochastic Processes and their Applications 2015
The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a mul- tifractal time-change of a CEBP process, where the time-change is ...
Added: January 12, 2015
Zhitlukhin M., Alexey Muravlev, Theory of Probability and Its Applications 2013 Vol. 57 No. 4 P. 708-717
This paper contains detailed exposition of the results presented in the short communication [M. V. Zhitlukhin and A. A. Muravlev, Russian Math. Surveys, 66 (2011), pp. 1012–1013]. We consider Chernoff’s problem of sequential testing of two hypotheses about the sign of the drift of a Brownian motion under the assumption that it is normally distributed. ...
Added: February 12, 2014
Каз. : Издательство «Фэн» Академии наук Республики Татарстан, 2013
Шестая всероссийская научно-практическая конференция «Имитационное моделирование. Теория и практика» ИММОД-2013 состоялась в Казани (Республика Татарстан) 16-18 октября 2013 года.
Научная программа конференции включала следующие тематические направления:
- теоретические основы и методология имитационного и комплексного моделирования;
- методы оценивания качества моделей полимодельных комплексов;
- методы и системы распределенного моделирования;
- моделирование глобальных процессов;
- средства автоматизации и визуализации имитационного моделирования;
- системная динамика ...
Added: December 8, 2013
Zhitlukhin M., Shiryaev A., Theory of Probability and Its Applications 2013 Vol. 57 No. 3 P. 497-511
We formulate a general Bayesian disorder detection problem, which generalizes models considered in the literature. We study properties of basic statistics, which allow us to reduce problems of quickest detection of disorder moments to optimal stopping problems. Using general results, we consider in detail a disorder problem for Brownian motion on a finite time segment. ...
Added: March 9, 2014
Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60-81
We find precise small deviation asymptotics for some Brownian functionals in the weighted Hilbert norm without knowing of eigenfunctions of corresponding integral Fredholm operators. As particular cases we find for the first time the small deviation asymptotics of Brownian excursion and Brownian meander. ...
Added: January 30, 2015
Tamm M., Majumdar S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 P. 021135
We compute analytically the mean number of common sites, WN(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N−d) plane, there are three distinct regimes for the asymptotic large-t growth of WN(t). These three regimes are separated by two critical lines d=2 and d=dc(N)=2N/(N−1) in the (N-d) plane. For d<2, WN(t)∼td/2 for large t (the N dependence is ...
Added: November 18, 2013
A. A, Gushchin, Urusov M. A., Russian Mathematical Surveys 2019 Vol. 74 No. 5 P. 953-955
We prove that a right-continuous integrable stochastic process admits a minimal embedding in the standard Brownian motion if and only if it is a submartingale or supermartingale. ...
Added: July 20, 2020
Kim K. O., Choi B. H., Jung K. T. et al., Journal of Coastal Research 2013 Vol. 65 P. 284-289
Three-dimensional simulation of 2011 East Japan-off Pacific coast earthquake tsunami induced vortex flows in the Oarai port. ...
Added: November 23, 2013
Nikitin Ya. Yu., Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60-81
We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not assume the knowledge of eigenfunctions of the correspondinge covariance operator. This makes it possible to generalize many previous results in this area. We also obtain ultimate results connected with exact small deviation of Brownian ...
Added: February 28, 2015
Tamm M., Stadnichuk V., Ilyina A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2014 Vol. 89 P. 042137
We consider two random walkers starting at the same time t = 0 from different points in space separated by a given distance R. We compute the average volume of the space visited by both walkers up to time t as a function of R and t and dimensionality of space d. For d < 4, this volume, after proper renormalization, is shown to be ...
Added: May 23, 2014
Zhitlukhin M., Муравлев А. А., Shiryaev A., Russian Mathematical Surveys 2013 Vol. 68 No. 2 P. 389-394
We find the exact optimal decision rule in the problem of testing two hypotheses about the drift of a Brownian motion in the setting of Kiefer and Weiss. ...
Added: March 9, 2014
Protasov V., Voinov A. S., Sbornik Mathematics 2015 Vol. 206 No. 7 P. 921-940
We analyze compact multiplicative semigroups of affine operators acting in a finite-dimensional space. The main result states that every such semigroup is either contracting, that is, contains elements of arbitrarily small operator norm, or all its operators share a common invariant affine subspace on which this semigroup is contracting. The proof uses functional difference equations ...
Added: March 11, 2017
Kim D. C., Kim K. O., Choi B. H. et al., Journal of Coastal Research 2013 Vol. 65 P. 272-277
Three-dimensional runup simulation of the 2004 Indian Ocean tsunami at the Lhok Nga Twin Peaks. ...
Added: November 22, 2013
Kim D. C., Kim K. O., Didenkulova I. et al., Journal of Coastal Research 2013 Vol. 65 P. 266-271
Three-dimensional tsunami runup simulation at the Koborinai port, Sanriku coast, Japan. ...
Added: November 22, 2013
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018