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On large deviations in the averaging principle for SDE’s with a ``full dependence’’, revisited
Discrete and Continuous Dynamical Systems - Series B. 2013. Vol. 18. No. 2. P. 523-549.
Veretennikov A.
Priority areas:
mathematics
Language:
English
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
Yanovich Y., Proceedings of Machine Learning Research 2017 Vol. 60 P. 18-38
In many applications, the real high-dimensional data occupy only a very small part in the high dimensional ‘observation space’ whose intrinsic dimension is small. The most popular model of such data is Manifold model which assumes that the data lie on or near an unknown manifold (Data Manifold, DM) of lower dimensionality embedded in an ...
Added: June 15, 2017
Mariani M., Probability Theory and Related Fields 2010 Vol. 147 No. 3–4 P. 607-648
Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions ...
Added: December 4, 2017
M.V.Karasev, E.M.Novikova, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 4 P. 463-468
We study dynamics of a charge in the planar Penning trap in which the direction of magnetic field does not coincide with the trap axis. Under some combined resonance condition on the deviation angle and magnitudes of magnetic and electric fields, the trajectories of a charge are near-periodic. We describe the reduction to a top-like ...
Added: October 22, 2015
V. G. Danilov, R. K. Gaydukov, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 431-455
A problem of a nonstationary incompressible viscous fluid ow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or triple-deck structure boundary layers on ...
Added: August 19, 2020
Pechersky E., Pirogov S. A., Schütz G. M. et al., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 107-120
We study a class of random processes on N particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through ...
Added: December 5, 2020
Mariani M., Zambotti L., Advances in Applied Probability 2016 Vol. 48 No. 3 P. 648-671
A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of ...
Added: December 10, 2017
Anikin A. Y., Brüning J., Dobrokhotov S. et al., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 265-276
In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can ...
Added: September 18, 2019
Gribkova N., Probability and Mathematical Statistics 2017 Vol. 37 No. 1 P. 101-118
In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. (1982) – the first and, as far as we know, the single article where some results ...
Added: February 28, 2020
Gribkova N., Mathematical Methods of Statistics 2016 Vol. 25 No. 4 P. 313-322
We establish Cramér type moderate deviation results for heavy trimmed L-statistics; we obtain our results under a very mild smoothness condition on the inversion F −1 (F is the underlying distribution function of i.i.d. observations) near two points, where trimming occurs, we assume also some smoothness of weights of the L-statistic. Our results complement previous work on Cramér type large deviations ...
Added: February 28, 2020
Nikitin Y. Y., Ragozin I. A., Vestnik St. Petersburg University: Mathematics 2019 Vol. 52 No. 2 P. 169-177
The logistic family of distributions belongs to the class of important families in the theory of probability and mathematical statistics. However, the goodness-of-fit tests for the composite hypothesis of belonging to the logistic family with unknown location parameter against the general alternatives have not been sufficiently explored. We propose two new goodness-of-fit tests: the integral ...
Added: October 1, 2019
Volk D., Liverani C., De Simoi J. et al., Journal of Statistical Physics 2016
We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Freidlin-Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the ...
Added: October 11, 2016
V.V. Litvinova, Ya. Yu. Nikitin, Journal of Mathematical Sciences 2016 Vol. 219 No. 5 P. 782-788
Some new U-empirical tests for normality of Kolmogorov type based on the famous Polya's characterization are build and explored. Their local asymptotic efficiency in Bahadur sense is calculated. ...
Added: November 5, 2016
Shirokov D., Advances in Applied Clifford Algebras 2017 Vol. 27 No. 1 P. 149-163
In this paper we consider different operators acting on Clifford algebras. We consider Reynolds operator of Salingaros’ vee group. This operator “average” an action of Salingaros’ vee group on Clifford algebra. We consider conjugate action on Clifford algebra. We present a relation between these operators and projection operators onto fixed subspaces of Clifford algebras. Using ...
Added: September 27, 2016
Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109
A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was
considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with
induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to
construct a numerical algorithm for solving these equations with ...
Added: June 10, 2020
Bogachev V., 2020 Vol. 75 No. 3 P. 393-425
Generalizations and refnements are given for results of Kozlov and Treschev on non-uniform averagings in the ergodic theorem in the case of operator semigroups on spaces of integrable functions and semigroups of
measure-preserving transformations. Conditions on the averaging measures are studied under which the averages converge for broad classes of integrable functions. ...
Added: October 23, 2020
Nikitin Y. Y., Volkova K. Y., Mathematical Methods of Statistics 2016 Vol. 25 No. 1 P. 54-66
We build new tests of composite hypothesis of exponentiality which are functionals of U-empirical measures and which are closely related and inspired by some special property of exponential law. We study limiting distributions, large deviations and asymptotic efficiency of new tests. Most favorable alternatives are described. Finally we reject using our test the hypothesis on ...
Added: March 23, 2016
Nikitin Y. Y., Volkova K. Y., Journal of Mathematical Sciences 2014 Vol. 199 No. 2 P. 130-138
We construct and study new goodness-of-fit tests for the power distribution based on the Puri-Rubin characterization and using U-empirical distribution functions. We describe their limiting distributions and large deviations. Next we find their local Bahadur efficiency for common alternatives and study the conditions of local optimality. ...
Added: February 10, 2015
Danilov V., European Journal of Mechanics - B/Fluids 2019 Vol. 74 P. 152-158
A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability
is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed. ...
Added: October 21, 2018
Nikitin Ya. Yu., Ahsanullah M., Dordrecht, L., Heidelberg, NY : Springer, 2015
We use the characterization of distribution symmetry in terms of order statistics in order to obtain new tests of symmetry based on U-empirical distribution functions. We calculate their limiting distributions and large deviations and explore their local Bahadur efficiency against location alternatives which turns out to be rather high. ...
Added: April 14, 2015
Polyak B. T., Tremba A. A., Khlebnikov M. V. et al., Automation and Remote Control 2015 Vol. 76 No. 6 P. 957-976
Research in the transient response in linear systems with nonzero initial conditions was initiated by A.A. Feldbaum in his pioneering work [1] as early as in 1948. However later, studies in this direction have faded down, and since then, the notion of transient process basically means the response of the system with zero initial conditions ...
Added: October 23, 2015
Pechersky E. A., Pirogov S. A., Schütz G. M. et al., Theoretical and Mathematical Physics 2019 Vol. 198 No. 1 P. 118-128
We consider a system of N identical independent Markov processes, each taking values 0 or 1. The system describes the stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux action, each atom changes its state with some rates either from its ground state (state 0) to the excited ...
Added: December 5, 2020
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013