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Метод параметрикса для диффузий и цепей Маркова
Konakov V., Markova A., Автоматика и телемеханика 2015 № 10 С. 74-89
We consider a sequence of Markov chains that weakly converge to a diffusion process. We assume that the trend contains a linearly growing component. The usual parametrix method does not apply since the trend is unbounded. We show how to modify the parametrix method in order to get local limit theorems in this case. ...
Added: December 10, 2014
Konakov V., Woerner J., Mammen E., Bernoulli: a journal of mathematical statistics and probability 2014 Vol. 20 No. 2 P. 623-644
We assume that a high frequency Markov chain runs in the background on a very fine time grid but that it is only observed on a coarser grid. In this paper we show that under appropriate conditions the L1 distance between the joint distribution of the Markov chain and the distribution of the discretized diffusion ...
Added: November 13, 2013
Albeverio S., Danilov V., Mathematische Nachrichten 2012 Vol. 285 No. 4 P. 426-439
Using an idea going back to Madelung, we construct global in time solutions to the transport equation corresponding to the asymptotic solution of the Kolmogorov-Feller equation describing a system with diffusion, potential and jump terms. To do that we use the construction of a generalized delta-shock solution of the continuity equation for a discontinuous velocity ...
Added: December 24, 2012
Konakov V., Menozzi S., Molchanov S., Annales de l’Institut Henri Poincaré 2010 Vol. 46 No. 4 P. 908-923
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of McKean-Singer type for the density. We there from derive an explicit Gaussian upper bound and a partial lower bound that characterize the additional singularity ...
Added: December 4, 2012
Mikhail Batsyn, Kalyagin V. A., Springer Proceedings in Mathematics & Statistics 2012 Vol. 32 P. 51-64
The distribution of the sum of independent random variables plays an important role in many problems of applied mathematics. In this paper we concentrate on the case when random variables have a continuous distribution with a discontinuity (or a probability mass) at a certain point r. Such a distribution arises naturally in actuarial mathematics when ...
Added: October 9, 2012
Budkov Y., Kolesnikov A. L., Journal of Statistical Mechanics: Theory and Experiment 2016 Vol. 2014 P. 1-12
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and potential energy in the parabolic well. In both cases we obtain the exact relations for the characteristic function ...
Added: October 27, 2016
Bogachev V., Veretennikov A., Shaposhnikov S., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 460 № 5 С. 507-511
Методами уравнений в частных производных установлены достаточные условия дифференцируемости инвариантных мер диффузионных процессов по параметру ...
Added: October 11, 2015
Konakov V., Mammen E., Probability Theory and Related Fields 2009 Vol. 143 No. 1 P. 137-176
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are motivated by ...
Added: December 4, 2012
Veretennikov A., Теорiя Ймовiрностей та Математична Статистика 2016 Vol. 95 P. 178-188
Poisson equation in the whole space was studied earlier for so called ergodic generators L corresponding to homogeneous Markov diffusions. Solving this equation is one of the main tools for diffusion approximation in the theory of stochastic averaging and homogenisation. Here a similar equation with a potential is considered, firstly because it is natural for ...
Added: October 17, 2017
Batsyn M. V., Kalyagin V. A., Научно-технический вестник Санкт-Петербургского государственного университета информационных технологий, механики и оптики 2008 № 51 С. 361-372
В работе исследована проблема вычисления функции распределения суммы страховых выплат при наличии эксцедентного перестрахования больших ущербов по индивидуальным страховым контрактам. Получено аналитическое выражение для этой функции при равномерном распределении ущерба в одном страховом случае. Для решения этой задачи использована однопериодная модель коллективных рисков. ...
Added: October 9, 2012
Kashtanov V., Kondrashova E. V., Надежность 2012 № 1 (40) С. 52-68
The present paper analyses characteristics of an input flow controlled by Markov chain. At the base of construction of the given flow rests the model of semi-Markov process. The paper has stated and proved the theorem about stationarity of an input flow controlled by Markov chain. In addition to that the theorem proved that in ...
Added: February 25, 2013
Batsyn M. V., Kalyagin V. A., Вестник Тверского государственного университета. Серия: Прикладная математика 2009 № 3 С. 81-100
В работе рассматривается задача определения распределения суммарных страховых выплат при перестраховании индивидуальных рисков в случае равномерного распределения ущерба по каждому страховому случаю. Основным результатом работы является аналитическое выражение функции распределения суммарных выплат. Полученный результат может быть использован для оценки точности определения оптимального уровня собственного удержания на основе нормальной аппроксимации. ...
Added: October 9, 2012
Konakov V., Menozzi S., Journal of Theoretical Probability 2011 Vol. 24 No. 2 P. 454-478
Consider a multidimensional stochastic differential equation governed by a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to a time step ...
Added: December 4, 2012
Konakov V., Mammen E., / Cornell University. Series arXiv "math". 2023. No. 2304.10673.
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit distributions approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for ...
Added: April 24, 2023
Konakov V., Mammen E., Bernoulli: a journal of mathematical statistics and probability 2005 Vol. 11 No. 4 P. 591-641
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. We prove Edgeworth-type expansions of order o(n-1-δ),δ>0, for transition densities. For this purpose we apply the parametrix method to represent the transition density as a functional of densities of sums of independent and identically distributed variables. Then we apply Edgeworth expansions ...
Added: December 4, 2012
Enatskaya N., М. : Юрайт, 2017
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Added: December 22, 2017
Goryainova E. R., Goryainov V. B., Наука и образование: электронное научно-техническое издание 2011 № 10
Для процесса 2D-авторегрессии порядка (1,1) устанавливается асимптотическая нормальность М-оценок с необязательно выпуклой функцией потерь. При помощи компьютерного моделирования устанавливается устойчивость этих оценок при засорении наблюдений грубыми выбросами. ...
Added: November 29, 2012
Lipatov M., Вестник Московского университета. Серия 1: Математика. Механика 2010 № 5 С. 61-64
The paper proves the recurrence of measurable cocycles with values in the subgroup of SL(2, C) of diagonal and skew-diagonal matrices over an ergodic transformation preserving the probability measure. ...
Added: November 15, 2012
Konakov V., Mammen E., Probability Theory and Related Fields 2000 Vol. 117 No. 4 P. 551-587
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved. ...
Added: October 15, 2012
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
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