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Talagrand Concentration Inequalities for Stochastic Partial Differential Equations

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Davar Khoshnevisan, Andrey Sarantsev

Probability · Submitted 20 Sep 2017

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

The authors' main claim Here, we develop a similar theory for some stochastic partial differential equations.

how it is stated · asserted 0.98 read the record →

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arXiv ID1709.07098 (version 3)
Pith ID6DH2NXUB, Pith's permanent record of this paper and its review
CitationAndrey Sarantsev, Davar Khoshnevisan. "Talagrand Concentration Inequalities for Stochastic Partial Differential Equations." arXiv:1709.07098 (2017). https://pith.science/paper/6DH2NXUB
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,461 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.20 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.

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 One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. background 1.00 0.04 0.05 asserted 0.75
s1 That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. background 0.99 0.05 0.03 asserted 0.97
s2 Such transportation-information inequalities were recently established for some stochastic differential equations. background 0.99 0.05 0.04 asserted 1.00
s3 Here, we develop a similar theory for some stochastic partial differential equations. contribution 1.00 0.93 0.63 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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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

One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.

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3 arXiv papers cite this in 6 sentences

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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Cites it as background 1 paper
  • Afterwards, TCI inequalities were established for discrete-time Markov chains, [ref] ; for discrete-time stationary processes, [ref] ; for stochastic ordinary differential equations driven by Brownian motion [ref] and by more general noise [ref] ; for stochastic partial differential equations, [ref] , and for neutral stochastic equations (which depend on past history) [ref] .

    A Note on Transportation Cost Inequalities for Diffusions with Reflections · Introduction and Main Results · 0.94

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