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Markov chains, AR models, and regular variation

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Piotr Dyszewski, Tamara Mika

Probability · Submitted 22 Oct 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that the precise structure of the underlying chain affects the form of the associated spectral measure.

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arXiv ID2510.19312 (version 2)
Pith IDGUGARJV7, Pith's permanent record of this paper and its review
CitationPiotr Dyszewski, Tamara Mika. "Markov chains, AR models, and regular variation." arXiv:2510.19312 (2025). https://pith.science/paper/GUGARJV7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,559 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.60 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary distribution can be derived from that of the innovations, provided that the chain satisfies a certain monotonicity condition with respect to a gauge function. In the second part, we study random linear models with random coefficients defined by an explicit iterative scheme. We prove that the precise structure of the underlying chain affects the form of the associated spectral measure.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. contribution 0.96 0.88 0.09 asserted 0.63
s1 In the first part, we show that the regular variation of the stationary distribution can be derived from that of the innovations, provided that the chain satisfies a certain monotonicity condition with respect to a gauge function. result 0.95 0.94 0.31 asserted 1.00
s2 In the second part, we study random linear models with random coefficients defined by an explicit iterative scheme. contribution 0.81 0.82 0.04 asserted 0.77
s3 We prove that the precise structure of the underlying chain affects the form of the associated spectral measure. result 1.00 0.90 0.34 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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not examined
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  • references and citing sentences
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary distribution can be derived from that of the innovations, provided that the chain satisfies a certain monotonicity condition with respect to a gauge function. In the second part, we study random linear models with random coefficients defined by an explicit iterative scheme. We prove that the precise structure of the underlying chain affects the form of the associated spectral measure.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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