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Limits of Kalman Filter application in heavy tailed problems
Cornell University
,
2015.
№ 1505.07981.
Konakov V., Mozgunov P.
In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are replaced by components with alpha-stable distribution with di erent parameters alpha and beta. We consider the case when "all parameters are known"and two methods of parameters estimation are compared: the maximum likelihood estimator (MLE) and the expectation- maximization algorithm (EM). It was shown that in cases of large deviation from Gaussian distribution the total error of states estimation rises dramatically.We conjecture that it can be explained by underestimation of the state equation noises covariance matrix that can be taken into account through the EM parameters estimation and ignored in the case of ML estimation
Publication based on the results of:
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 ...
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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, ...
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Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
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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.
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Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
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Added: January 15, 2026
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Added: December 25, 2025
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We prove that the variety of flexes of algebraic curves
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Added: December 16, 2025
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We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
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Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
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Deviatov R., Baek S., / Series arXiv "math". 2025.
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...
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Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
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Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Prokhorov Y., / Series arXiv "math". 2025.
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Amerik E., Verbitsky M., Soldatenkov A., / Series arXiv "math". 2025.
Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction ...
Added: December 1, 2025
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Added: September 24, 2025
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Added: February 14, 2024
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Deryugina E., Maria Guseva, Alexey Ponomarenko, Journal of Central Banking Theory and Practice 2022 Vol. 11 No. 1 P. 87–104
We conduct a Monte Carlo experiment using an ad-hoc New Keynesian model and a tractable agent-based model to generate artificial credit cycle episodes. We show that fluctuations in the implicit measures of the natural rate of interest obtained using a conventional trivariate Kalman filter on these artificial datasets occur in the vicinity of credit cycle ...
Added: January 31, 2023
Zinchenko D., Zinchenko A., E. Nikonov, Physics of Particles and Nuclei 2022 Vol. 53 No. 2 P. 519 –523
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Added: January 12, 2023
Marino L., Menozzi S., Priola E., Studia Mathematica 2022 Vol. 267 No. 3 P. 321–346
We consider a possibly degenerate Kolmogorov Ornstein–Uhlenbeck operator of the form L=Tr(BD2)+⟨Az,D⟩, where A, B are N×N matrices, z∈RN, N≥1, which satisfy the Kalman condition which is equivalent to the hypoellipticity condition. We prove the following stability result: the Schauder and Sobolev estimates associated with the corresponding parabolic Cauchy problem remain valid, with the same constant, for the parabolic Cauchy problem associated with ...
Added: November 10, 2022