Global limit theorems on the convergence of multidimensional random walk to stable processes

S. Molchanov; Agbor A.; Vainberg B.

Publications

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Global limit theorems on the convergence of multidimensional random walk to stable processes

Stochastics and Dynamics. 2016. P. 1–14.

Molchanov S., Agbor A., Vainberg B.

Language: English

Keywords: характеристические функции global convergence stable distributions characteristic functions глобальная сходимость устойчивые распределения

Publication based on the results of:

Вероятностные и статистические методы анализа сложных моделей, задаваемых стохастическими дифференциальными и разностными уравнениями (2015)

Метод Стейна и характеристические функции

Tikhomirov A., Успехи математических наук 2025 Т. 80 № 4(484) С. 121–172

В работе дается обзор различных приложений метода описания аппроксимирующих распределений с помощью дифференциальных уравнений для характеристических функций и, в частности, применений этого описания к оценке близости распределений. Эта идея впервые была предложена автором в 1976 г. В дальнейшем такой подход, в последнее время называемый некоторыми авторами методом Стейна–Тихомирова (см., например, работы П. Айхельсбахера, В. Редносса, ...

Added: November 10, 2025

Achieving Global Convergence? Integrating disruptive technologies within evolving SME business models: A micro-level lens

Scuotto V., Crammond R. J., Murray A. et al., Journal of International Management 2023 Vol. 29 No. 6 P. 1–17

This research responds to the call on global convergence in the international business management domain. Global convergence requires new evolutionary, devolutionary and even revolutionary strategies that are framed in the context of digital transformation. The digital transformation phenomenon has led to different theoretical and managerial perspectives on disruptive technologies provoking the need for more studies ...

Added: May 28, 2025

Об одном вероятностном свойстве фейеровских пар или об одном классе характеристических функций вероятностных распределений

Соболев В. Н., Кондратенко А. Е., Елизарова Н. А., В кн.: XXX Международная конференция «Математика. Экономика. Образование». XIV Международный симпозиум «Ряды Фурье и их приложения».: Ростов н/Д: Южный федеральный университет, 2024. С. 34.

Added: February 8, 2025

Optimization in complex spaces with the mixed Newton method

Bakhurin S., Hildebrand R., Alkousa M. et al., Journal of Global Optimization 2024 Vol. 90 P. 373–399

We propose a second-order method for unconditional minimization of functions $f(z)$ of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger derivative $\frac{\partial^2f}{\partial\bar z\partial z}$ for computation of the search direction, as opposed to the full Hessian $\frac{\partial^2f}{\partial(z,\bar z)^2}$ in the classical Newton method. The method has ...

Added: November 27, 2024

Cooperative Game-Theoretic Models of the Cournot Oligopoly

Korolev A. V., Ougolnitsky G. A., International Game Theory Review 2023 Vol. 25 No. 2 Article 2350004

In this paper, we build and investigate cooperative games with different characteristic functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot oligopoly game-theoretic models in normal form. Also, we build and investigate coop27 erative three-player games with the same characteristic ...

Added: January 26, 2023

Limit theorems for the alloy-type random energy model

Molchanov S., Panov V., Stochastics-An International Journal of Probability and Stochastic Processes 2019 Vol. 91 No. 5 P. 754–772

In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, ...

Added: November 19, 2018

Distribution of linear statistics of singular values of the product of random matrices

Goetze F., Naumov A.A., Tikhomirov A., Bernoulli: a journal of mathematical statistics and probability 2017 Vol. 23 No. 4B P. 3067–3113

In this paper we consider the product of two independent random matrices X^(1) and X^(2). Assume that X_{jk}^{(q)},1\le j,k \le n,q=1,2,, are i.i.d. random variables with \EX_{jk}^{q}=0, VarX_{jk}^{(q)}=1/ Denote by s_1(W),…,s_n(W) the singular values of W:=n^{-1}X^(1)X^(2). We prove the central limit theorem for linear statistics of the squared singular values s_1^2(W),…,s_n^2(W) showing that the limiting variance depends on \kappa_4:=\E(X_{11}^{(1)})^4−3. ...

Added: April 28, 2018

Limit theorems for sums of random variables with mixture distribution

Panov V., Statistics and Probability Letters 2017 Vol. 129 P. 379–386

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...

Added: July 10, 2017

Limit theorems for sums of random variables with mixture distribution

Panov V., / Series arXiv "math". 2017. No. 1703.10463.

Added: March 31, 2017

Economic Cycles, Crises, and the Global Periphery

Korotayev A., Grinin L. E., Tausch A., Springer, 2016.

This thought-provoking monograph analyzes long- medium- and short-term global cycles of prosperity, recession, and depression, plotting them against centuries of important world events. Major research on economic and political cycles is integrated to clarify evolving relationships between the global center and its periphery as well as current worldwide economic upheavals and potential future developments. Central ...

Added: October 15, 2016

О характеристических функциях многочленов от случайных величин

Ulyanov V. V., Гетце Ф., Прохоров Ю. В., В кн.: Ю.В.Прохоров. Избранные труды.: М.: Торус Пресс, 2012. С. 646–648.

Исследованы свойства характеристических функций многочленов от случайных величин ...

Added: May 2, 2014