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Optimal control of infinite-dimensional differential systems with randomness and path-dependence and stochastic path-dependent Hamilton-Jacobi equations

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Jinniao Qiu, Yang Yang

Optimization and Control · Submitted 17 Jul 2023

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

The authors' main claim A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

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arXiv ID2307.08882 (version 1)
Pith IDGP6LFKPA, Pith's permanent record of this paper and its review
CitationJinniao Qiu, Yang Yang. "Optimal control of infinite-dimensional differential systems with randomness and path-dependence and stochastic path-dependent Hamilton-Jacobi equations." arXiv:2307.08882 (2023). https://pith.science/paper/GP6LFKPA
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,630 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.02 · states quantitative result 0.03 · compares with prior results 0.93 · mentions code or data availability 0.02.

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

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018), 2096--2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

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 This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. background 0.50 0.59 0.05 asserted 0.96
s1 As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. background 0.84 0.06 0.03 asserted 0.62
s2 Anal. 275 (2018), 2096--2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. result 0.85 0.81 0.35 asserted 1.00
s3 A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation. result 0.63 0.94 0.71 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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  • C citations
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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

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Original abstract

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018), 2096--2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

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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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  • Our previous works Qiu [ref] , Qiu and Wei [ref] , Qiu and Zhang [ref] , Qiu and Yang [ref] addressed this problem, and extended it to several other cases, including the basic case on $ℝ^d$, the case of stochastic differential game on $ℝ^d$ and the case of controlled ordinary differential equations with random path-dependent coefficients in finite and infinite dimension.

    A Viscosity Solution Theory of Stochastic Hamilton-Jacobi-Bellman equations in the Wasserstein Space · Introduction · 0.80

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