?
The Brownian motion on Aff(R) and quasi-local theorems
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 in
tegrating those return probabilities on a suitable neighborhood of the origin,
the expected polynomial decay is restored. This is what we call a Quasi-local
theorem.
In book
Canzani Y., Chen L., Jakobson D. Vol. 739: Probabilistic Methods in Geometry, Topology and Spectral Theory. , AMS, 2019
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
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
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
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
Rossokhin V. V., Финансы и кредит 2014 № 26 (602) С. 31-38
In the financial sector the problem of predicting price movements and risk prediction have a double meaning: the development of client portfolio management business and analysis of financial market participant activity.
The research is based on the postulate of random nature of price walk. Consequently, the basic model used to predict the price movements of assets ...
Added: March 18, 2014
Kelbert M., Konakov V., Menozzi S., Stochastic Processes and their Applications 2016 Vol. 126 P. 1145-1183
We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of ...
Added: March 21, 2016
Korolev A. V., Automation and Remote Control 2022 Vol. 13 No. 1 P. 483-501
Stochastic parameters are introduced into a model of network games with production and knowledge externalities. The model was formulated by V. Matveenko and A. Korolev and generalizes Romer’s two-period model. The agents’ productivities have both deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle that ...
Added: April 22, 2022
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
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
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
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
Zhitlukhin M., Муравлев А. А., Теория вероятностей и ее применения 2012 Т. 57 № 4 С. 778-788
Работа содержит подробное изложение результатов, представленных ранее в кратком сообщении авторов (Успехи математических наук, 2011). Рассматривается задача Чернова последовательной проверки гипотез о положительности или отрицательности сноса броуновского движения в предположении, что он имеет нормальное распределение. Выводится интегральное уравнение, характеризующее оптимальное решающее правило, и численно находится его решение. Полученный результат дополняет результаты работ Г. Чернова и ...
Added: March 9, 2014
Korolev A. V., Математическая теория игр и ее приложения 2021 № 1 С. 102-129
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which ...
Added: May 15, 2021
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 Proceedings. Vol. 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
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
Safdari H., Cherstvy A., Chechkin A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 95 P. 012120-1-012120-15
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic,and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call thisstochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate howthe mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by ...
Added: April 18, 2019
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
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
Decrouez G. G., Jones O. D., The Annals of Applied Probability 2012 Vol. 22 No. 6 P. 2357-2387
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 ...
Added: September 29, 2014
Safonov A. V., Agudov N. V., Krichigin A. V. et al., Journal of Statistical Mechanics: Theory and Experiment 2020 Vol. 2020 P. 024003
We propose a stochastic model for a memristive system by
generalizing known approaches and experimental results. We validate our
theoretical model by experiments carried out on a memristive device based
on Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti multilayer structure. In the framework
of the proposed model we obtain the exact analytic expressions for stationary
and nonstationary solutions. We analyze the equilibrium and non-equilibrium
steady-state distributions of ...
Added: December 14, 2022
Korolev A. V., , in : Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2019. : Birkhauser/Springer, 2020. Ch. 6. P. 65-85.
In this paper we introduce stochastic parameters into the network game
model with production and knowledge externalities. This model was proposed
by V. Matveenko and A. Korolev as a generalization of the two-period Romer
model. Agents differ in their productivities which have deterministic and stochastic
(Wiener) components. We study the dynamics of a single agent and the dynamics
of a ...
Added: November 30, 2020
Nikitin Y. Y., Пусев Р. С., Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 98-123
Найдена точная асимптотика малых уклонений в гильбертовой норме ряда процессов, связанных с броуновским движением, в частности, броуновской экскурсии, броуновского меандра и броуновского локального времени. ...
Added: November 26, 2013
Korolev A. V., , in : Frontiers of Dynamic Games: Game Theory and Management, St. Petersburg, 2020. : Cham : Birkhäuser, 2021. P. 167-187.
Added: April 5, 2022
Бородин А. Н., Journal of Mathematical Sciences 2022 Vol. 268 No. 5 P. 599-611
Added: December 6, 2022