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Existence And Uniqueness Of Stationary Solution Of Nonlinear Stochastic Differential Equation With Memory

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Yuri Bakhtin

Probability · Submitted 29 Jan 2002

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

The authors' main claim Sufficient conditions for existence and uniqueness of stationary solution are given.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0201275 (version 1)
Pith IDAKVOQKYB, Pith's permanent record of this paper and its review
CitationYuri Bakhtin. "Existence And Uniqueness Of Stationary Solution Of Nonlinear Stochastic Differential Equation With Memory." arXiv:math/0201275 (2002). https://pith.science/paper/AKVOQKYB
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,795 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.03 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary solution are given.

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 A stochastic differential equation with infinite memory is considered. background 0.82 0.36 0.03 asserted 0.95
s1 The drift coefficient of the equation is a nonlinear functional of the past history of the solution. background 0.81 0.27 0.03 asserted 1.00
s2 Sufficient conditions for existence and uniqueness of stationary solution are given. result 0.67 0.90 0.87 asserted 1.00

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

What was examined, and what was not

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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

A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary solution are given.

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