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Backward multivalued McKean-Vlasov SDEs and associated variational inequalities

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Jun Gong, Huijie Qiao

Probability · Submitted 21 Oct 2021

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

The authors' main claim Finally, we give a probabilistic interpretation for viscosity solutions of nonlocal quasi-linear parabolic variational inequalities.

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arXiv ID2110.11484 (version 3)
Pith IDQEV36QVM, Pith's permanent record of this paper and its review
CitationHuijie Qiao, Jun Gong. "Backward multivalued McKean-Vlasov SDEs and associated variational inequalities." arXiv:2110.11484 (2021). https://pith.science/paper/QEV36QVM
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,492 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it is presented that their solutions depend continuously on the terminal values. Finally, we give a probabilistic interpretation for viscosity solutions of nonlocal quasi-linear parabolic variational inequalities.

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 The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. background 0.73 0.38 0.04 asserted 0.93
s1 First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. result 0.71 0.95 0.31 asserted 1.00
s2 Then, it is presented that their solutions depend continuously on the terminal values. result 0.99 0.81 0.09 asserted 1.00
s3 Finally, we give a probabilistic interpretation for viscosity solutions of nonlocal quasi-linear parabolic variational inequalities. interpretation 0.52 0.91 0.53 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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  • references and citing sentences
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  • P abstract
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  • S sections
  • 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

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it is presented that their solutions depend continuously on the terminal values. Finally, we give a probabilistic interpretation for viscosity solutions of nonlocal quasi-linear parabolic variational inequalities.

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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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