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Multidimensional synchronization models based on Levy processes
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In book
Athens : ISAST: International Society for the Advancement of Science and Technology, 2015
Manita A., / Cornell University. Series "Working papers by Cornell University". 2014. No. arXiv:1409.2919.
http://xxx.tau.ac.il/abs/1409.2919 We propose stochastic N -component synchronization models, whose dynamics is described by Levy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components have limits in distribution as t→∞. We give conditions of existence of natural (intrinsic) space scales for large synchronized systemsю. It appears that ...
Added: March 18, 2015
Lubashevsky I., Friedrich R., Heuer A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 80 Article 031148
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to treat ...
Added: November 6, 2021
Lubashevsky I., Physica A: Statistical Mechanics and its Applications 2013 Vol. 392 No. 10 P. 2323-2346
The paper is devoted to the relationship between the continuous Markovian description of Lévy flights developed previously (see, e.g., I.A. Lubashevsky, Truncated Lévy flights and generalized Cauchy processes, Eur. Phys. J. B 82 (2011) 189–195 and references therein) and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of ...
Added: November 6, 2021
Belomestny D., Panov V., Electronic journal of statistics 2015 Vol. 9 No. 2 P. 1974-2006
In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type
\[
X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right),
\]
where \(\xi_s\) is a L{\'e}vy process. Our primal goal is to estimate the characteristics of the L\'evy process \(\xi\) from the low-frequency observations of the process \(X\). We present ...
Added: September 1, 2015
Manita A.D., Theory of Probability and Its Applications 2009 Vol. 53 No. 4 P. 155-165
We study the Markov exclusion process for a particle system with a local interaction in the integer strip. This process models the exchange of velocities and particle-hole exchange of the liquid molecules. It is shown that the mean velocity profile corresponds to the behavior which is characteristic for incompressible viscous liquid. We prove the existence ...
Added: June 20, 2017
М. : ИППИ РАН, 2013
Added: September 23, 2013
Finkelstein D., Kondratiev Y., Molchanov S. et al., Stochastics and Dynamics 2018 Vol. 18 No. 05 P. 1850037
We study stability of stationary solutions for a class of nonlocal semilinear parabolic equations. To this end, we prove the Feynman–Kac formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation ...
Added: November 14, 2019
Morozova E., Panov V., Applied Stochastic Models in Business and Industry 2023 Vol. 39 No. 6 P. 772-788
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Levy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the lowfrequency setup, which ...
Added: June 29, 2023
Lubashevsky I., The European Physical Journal B 2010 Vol. 82 P. 189-195
A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity ...
Added: November 6, 2021
Belomestny D., GUGUSHVILI S., SCHAUER M. et al., Communications in Mathematical Sciences 2019 Vol. 17 No. 3 P. 781-816
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the Levy density of a Levy process belonging to a flexible class of infinite activity subordinators. Posterior inference is performed via MCMC, and we circumvent the problem of the intractable likelihood via the data augmentation device, that ...
Added: June 11, 2019
Belomestny D., Trabs M., Annales de l'institut Henri Poincare (B) Probability and Statistics 2018 Vol. 54 No. 3 P. 1583-1621
The estimation of the diffusion matrix Σ of a high-dimensional, possibly time-changed Levy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on Σ. Applying a spectral approach, we construct a weighted least-squares estimator with nuclear-norm-penalisation. We prove oracle inequalities and derive convergence rates for ...
Added: May 5, 2018
Panov V., В кн. : Сборник статей конференции "Информационные технологии и системы" (ИТиС'12). : М. : ИППИ РАН, 2012.
This paper is devoted to studying the problem of the statistical inference on the activity of jumps for a class of the so-called time-changed Levy processes, i.e., for the processes in the form Ys = XT (s), where X is a Levy process and T is a non-negative and non-decreasing stochastic process, which is referred ...
Added: September 24, 2013
Morozova E., Panov V., / Cornell University. Series arXiv.org "q-fin.ST". 2022. No. 2210.13824.
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Lévy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the low-frequency setup, which ...
Added: October 26, 2022
Lubashevsky I., Friedrich R., Heuer A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 79 Article 011110
Based on multivariate Langevin processes we present a realization of Lévy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity-dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Lévy flights. Our procedure is similar to ...
Added: November 6, 2021
Panov V., , in : Сборник статей конференции Информационные технологии и системы (ИТиС'13). : М. : ИППИ РАН, 2013.
In this paper, we introduce a principally new method for modelling the dependence structure between two L{\'e}vy processes. The proposed method is based on some special properties of the time-changed Levy processes and can be viewed as an reasonable alternative to the copula approach. ...
Added: September 24, 2013
Belomestny D., Comte F., Genon-Catalot V. et al., Heidelberg : Springer, 2014
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Added: December 12, 2014
Lubashevsky I., Heuer A., Friedrich R. et al., The European Physical Journal B 2010 Vol. 78 P. 207-216
We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148 (2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously ...
Added: November 6, 2021
Kelbert M., Moreno-Franco H. A., SIAM Journal on Control and Optimization 2019 Vol. 57 No. 3 P. 2185-2213
In this paper, we guarantee the existence and uniqueness (in the almost everywhere
sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient
constraint and a partial integro-di erential operator whose Levy measure has bounded
variation. This type of equation arises in a singular control problem, where the state
process is a multidimensional jump-di usion with jumps of ...
Added: February 13, 2019
Belomestny D., Orlova T., Panov V., / Cornell University. Series arXiv "stat". 2017. No. 1702.02794.
We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax sense. ...
Added: February 10, 2017
Manita A., Journal of Physics: Conference Series 2016 Vol. 681 No. 1 P. 1-6
We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found ...
Added: March 29, 2016
Manita A., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012060 P. 1-7
L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from ...
Added: June 21, 2019
Gushchin A. A., Kordzakhia N., Novikov A., Statistical Inference for Stochastic Processes 2018 Vol. 21 No. 2 P. 363-383
We provide a full description of the class of translation invariant experiments with independent increments. Necessary and sufficient conditions for the weak convergence and the comparison of experiments within this class are given. Finally, we prove exponential boundedness of Pitman estimators in these models. ...
Added: June 29, 2018
Belomestny D., Orlova T., Panov V., Statistica Neerlandica 2019 Vol. 1 P. 100-117
We consider a new method of semiparametric statistical
estimation for the continuous-time moving-average Lévy
processes. We derive the convergence rates of the proposed
estimators and show that these rates are optimal in
minimax sense. ...
Added: April 28, 2018
Panov V., Markova A., В кн. : Математическое моделирование в экономике, страховании и управлении рисками: сборник материалов IV Международной молодежной научно-практической конференции. Т. 1.: Саратов : Издательство Саратовского университета, 2015. С. 171-176.
The article considers the procedure of constructing COGARCH volatility models with continuous time based on the Levy processes. The article describes the procedure of constructing the model in the general case and in the case of compound Poisson process. ...
Added: December 8, 2015