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Influence of the random walk finite step on the first-passage probability
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 first-passage probability from the exact function, which we attribute to the
finiteness of the random walk step.
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Lyulko Y., Theory of Probability and Its Applications 2010 Vol. 54 No. 3 P. 516–525
In this paper we consider the problems of finding stochastic representations of functional F = F(ω) of a random walk. We obtain both single and multiple representations of functionals FN = max k ≦ N Sk, Fτ-a = max k ≦ τ-a Sk, where τ-a is the time of the first reaching the level-a, a ∈ N, by a random walk. ...
Added: August 28, 2024
Lyulko Y., Теория вероятностей и ее применения 2009 Т. 54 № 3 С. 580–589
В работе исследованы вопросы отыскания стохастических представлений для функционалов F=F(ω) от случайного блуждания. Получены как обычные, так и многократные представления некоторых функционалов "максимального" типа. ...
Added: May 19, 2022
Karpov I., Glazkova E., , in: Recent Trends in Analysis of Images, Social Networks and Texts. 9th International Conference, AIST 2020, Skolkovo, Moscow, Russia, October 15–16, 2020 Revised Supplementary ProceedingsVol. 12602.: Springer, 2021. P. 11–21.
The widespread of Online Social Networks and the opportunity to commercialize popular accounts have attracted a large number of automated programs, known as artificial accounts. This paper (Project repository available at http://github.com/karpovilia/botdetection) focuses on the classification of human and fake accounts on the social network, by employing several graph neural networks, to efficiently encode attributes and ...
Added: June 19, 2021
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
Синцова К. А., https://ms.hse.ru/voronovo2019, 2019.
В данной работе исследуется модельная задача о стационарных вынужденных колебаниях жидкости при высокой частоте в поле силы тяжести в бесконечном бассейне с коническим дном. Получаются оценки малых установившихся гравитационных колебаний жидкости в окрестности конической точки и на бесконечности. ...
Added: December 6, 2019
Molchanov S., Vainberg B., SIAM Journal on Mathematical Analysis 2019 Vol. 51 No. 3 P. 1824–1835
Symmetric random walks in $R^d$ and $Z^d$ are considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all $x$ and $t$) asymptotic behavior at infinity of the transition probability (fundamental solution of the corresponding parabolic convolution operator) is found. ...
Added: November 14, 2019
V.L. Kreps, Automation and Remote Control 2019 Vol. 80 No. 2 P. 362–379
Using a simplified multistage bidding model with asymmetrically informed agents, De Meyer and Saley [17] demonstrated an idea of endogenous origin of the Brownian component in the evolution of prices on stock markets: random price fluctuations may be caused by strategic randomization of “insiders.” The model is reduced to a repeated game with incomplete information. ...
Added: May 7, 2019
Klimenkova O., Menshutin A., Shchur L., Computer Physics Communications 2019 Vol. 241 P. 28–32
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability ...
Added: April 9, 2019
Klimenkova O., Menshutin A., Shchur L., / Series arXiv "math". 2018. No. 1811.03788.
Added: November 12, 2018
Lebedev M., Пимашкин А. С., Ossadtchi A., Frontiers in Behavioral Neuroscience 2018 Vol. 12 No. 98 P. 1–8
According to the currently prevalent theory, hippocampal formation constructs and maintains cognitive spatial maps. Most of the experimental evidence for this theory comes from the studies on navigation in laboratory rats and mice, typically male animals. While these animals exhibit a rich repertoire of behaviors associated with navigation, including locomotion, head movements, whisking, sniffing, raring ...
Added: April 26, 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