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## Distributions of Functionals of the Local Time of Brownian Motion with Discontinuous Drift

Journal of Mathematical Sciences. 2022. Vol. 268. No. 5. P. 599-611.

Бородин А. Н.

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

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

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

Birkhauser/Springer, 2020

The content of this volume is mainly based on selected talks that were given at the
“International Meeting on Game Theory (ISDG12-GTM2019),” as joint meeting of
“12th International ISDG Workshop” and “13th International Conference on Game
Theory and Management,” held in St. Petersburg, Russia on July 03–05, 2019. The
meeting was organized by St. Petersburg State University and International ...

Added: November 30, 2020

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

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

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

A. A, Gushchin, Urusov M. A., Russian Mathematical Surveys 2019 Vol. 74 No. 5 P. 953-955

We prove that a right-continuous integrable stochastic process admits a minimal embedding in the standard Brownian motion if and only if it is a submartingale or supermartingale. ...

Added: July 20, 2020

Zhitlukhin M., Shiryaev A., Statistics and Decisions 2011 Vol. 38 No. 3 P. 227-249

Added: February 12, 2014

Zhitlukhin M., Муравлев А. А., Shiryaev A., Russian Mathematical Surveys 2013 Vol. 68 No. 2 P. 389-394

We find the exact optimal decision rule in the problem of testing two hypotheses about the drift of a Brownian motion in the setting of Kiefer and Weiss. ...

Added: March 9, 2014

Bodrova A., Chechkin A., Cherstvy A. et al., Scientific Reports 2016 Vol. 6 P. 1-16

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion ...

Added: April 18, 2019

Zhitlukhin M., Shiryaev A., Theory of Probability and Its Applications 2013 Vol. 57 No. 3 P. 497-511

We formulate a general Bayesian disorder detection problem, which generalizes models considered in the literature. We study properties of basic statistics, which allow us to reduce problems of quickest detection of disorder moments to optimal stopping problems. Using general results, we consider in detail a disorder problem for Brownian motion on a finite time segment. ...

Added: March 9, 2014

Nikitin Ya. Yu., Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60-81

We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not assume the knowledge of eigenfunctions of the correspondinge covariance operator. This makes it possible to generalize many previous results in this area. We also obtain ultimate results connected with exact small deviation of Brownian ...

Added: February 28, 2015

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

Konakov V., Menozzi S., Molchanov S., , in : Contemporary Mathematics. Vol. 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

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

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

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

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