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Стохастические представления функционалов “максимального” типа от случайного блуждания
Теория вероятностей и ее применения. 2009. Т. 54. № 3. С. 580–589.
Lyulko Y., Теория вероятностей и ее применения 2011 Т. 56 № 1 С. 167–176
Работа состоит из двух частей. В первой части с помощью строго марковского свойства показано, что в общем случае распределение времени пребывания будет геометрическим (с массой в нуле). В качестве примера рассмотрено скошенное случайное блуждание Sα=(Sαk)k≥0 с параметром α∈[0,1], для которого распределение времени пребывания найдено в явном виде.
Во второй части работы делается предельный переход от времени пребывания скошенного случайного блуждания к ...
Added: May 19, 2022
Nesterenko A., Khametov V., Труды Карельского научного центра Российской академии наук 2021 № 6 С. 49–58
В статье приведено решение задач об оптимальной остановке в ситуации, когда наблюдается случайное блуждание, а функция полезности наблюдателя --- экспоненциальная (конечный и бесконечный горизонт). Для этих задач найдено:
i) явное решение уравнения Беллмана;
ii) граница, разделяющая внутренность области остановки от области продолжения наблюдений;
iii) оптимальное правило остановки. ...
Added: November 27, 2020
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 ...
Added: December 30, 2019
Klimenkova O., Menshutin A., Shchur L., Journal of Physics: Conference Series 2018 Vol. 955 No. 012009 P. 1–6
A well known connection between first-passage probability of random walk and
distribution of electrical potential described by Laplace equation is studied. We simulate random
walk in the plane numerically as a discrete time process with fixed step length. We measure
first-passage probability to touch the absorbing sphere of radius R in 2D. We found a regular
deviation of the ...
Added: February 1, 2018
Maksimova O., Григорьев В. И., Компьютерные исследования и моделирование 2017 Т. 9 № 6 С. 905–918
Nowadays the random search became a widespread and effective tool for solving different complex optimization and adaptation problems. In this work, the problem of an average duration of a random search for one object by another is regarded, depending on various factors on a square field. The problem solution was carried out by holding total ...
Added: November 16, 2017
Konakov V., Menozzi S., Molchanov S., , in: Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference.: M.: RUDN, 2017. P. 202–206.
This note states several results on the exponential functionals of the Brownian motion and their approximations by Markov chains. Starting from M.Yor, such functionals were studied in mathematical finance. At the same time, they play a significant role in different settings: the analysis of diffusions on the class of solvable Lie groups, in particular on ...
Added: October 23, 2017
Kreps V. L., Математическая теория игр и ее приложения 2017 Т. 9 № 3 С. 3–35
With the help of a simplified model of multistage bidding with asymmetrically informed agents De Meyer and Saley demonstrate an idea of endogenous origin of Brownian component in the evolution of prices on stock markets: random price fluctuations may originate from strategic randomization of "insiders". The model is reduced to a repeated game with incomplete ...
Added: October 17, 2017
Khametov V., Yasonov E., В кн.: Современные методы и проблемы теории операторов и гармонического анализа и их приложения - VI.: Ростов н/Д: [б.и.], 2016. С. 143–144.
Предлагается минимаксный подход к решению задачи об оптимальной остановке. ...
Added: February 22, 2017
Blank M., Доклады Академии наук 2013 Т. 448 № 6 С. 629–632
We give conditions for unique ergodicity for a discrete time collective
random walk on a continuous circle. Individual particles in this collective
motion perform independent (and different) random walks conditioned
by the assumption that the particles cannot overrun each other.
Deterministic version of this system is studied as well. ...
Added: November 25, 2014