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Метод максимального правдоподобия в теореме де Финетти
Теория вероятностей и ее применения. 2018. Т. 63. № 4. С. 808–816.
Мелкумова Л. Э., Шатских С. Я.
De Finetti’s theorem states that the elements of an infinite exchangeable sequence of random variables are conditionally independent and identically distributed relative to some random variable (or a sigma-algebra generated by that random variable). In this work, we construct this random variable using the maximum likelihood method.
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
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
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Alexander Gushchin, Pavlyukevich I., Ritsch M., Statistical Inference for Stochastic Processes 2020 Vol. 23 No. 3 P. 553–570
We consider the problem of estimation of the drift parameter of an ergodic Ornstein–
Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed
continuously on a long time interval [0, T ], T →∞. We prove that the statistical model is
locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically
efficient. ...
Added: October 27, 2020
Soloveychik I., Trushin D., Wiesel A., IEEE Transactions on Signal Processing 2016 Vol. 64 No. 1 P. 244–257
In this paper, we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples of group symmetric structures include circulant, perHermitian, and proper quaternion matrices. We introduce a group symmetric version of Tyler's ...
Added: February 20, 2018
Artemov A., Burnaev E., Theory of Probability and Its Applications 2016 Vol. 60 No. 1 P. 126–134
We consider the problem of optimal estimation of the value of a vector parameter \thetavector=(\theta_0,...,\theta_n)^⊤ of the drift term in a fractional Brownian motion represented by the finite sum i=0^nii(t) over known functions \varphi_i(t), \alli. For the value of parameter \thetavector, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and ...
Added: January 23, 2018
Koldanov P., Koldanov A. P., Kalyagin V. A. et al., В кн.: Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : Proceedings, 23-27 October 2017.: M.: RUDN, 2017. С. 500–505.
Для проверки гипотезы об условной независимости в многомерном нормальном распределении широко используется тест, основанный на выборочном частном коэффициенте корреляции. В настоящей работе построен равномерно наиболее мощный несмещенный (РНМН) тест структуры Неймана проверки этой гипотезы. Показано, что построенный РНМН тест эквивалентен тесту, основанному на выборочном частном коэффициенте корреляции и, тем самым, тест частных корреляций является РНМН ...
Added: December 19, 2017
Koldanov P., Koldanov A. P., Kalyagin V. A. et al., Statistics and Probability Letters 2017 Vol. 122 P. 90–95
Model selection for Gaussian concentration graph is based on multiple testing of pairwise cinditional independence. In practical applications partial correlation tests are widely used. However it is not known whether partial correlation test is uniformly most powerful for pairwise conditional independence testing. This question is answered in the paper.Uniformly most powerful unbiased test of Neymann ...
Added: November 21, 2016
Vereshchagin N., Shen A., , in: Measures of Complexity. Festschrift for Alexey Chervonenkis.: Springer, 2015. P. 235–252.
A survey of main results in algorithmic statistics ...
Added: March 3, 2016
Kolesnikov A., Zaev D., / Series arXiv "math". 2015.
We study the Monge and Kantorovich transportation problems on R∞ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal transportation problem on the Hilbert space. We find sufficient conditions for convergence of finite-dimensional approximations to the Monge solution. The result holds, in particular, ...
Added: February 23, 2016