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Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces

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Giuseppina Guatteri, Gianmario Tessitore

Optimization and Control · Submitted 25 Apr 2014

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

The authors' main claim We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation.

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arXiv ID1404.6543 (version 2)
Pith IDWLGLRZBE, Pith's permanent record of this paper and its review
CitationGianmario Tessitore, Giuseppina Guatteri. "Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces." arXiv:1404.6543 (2014). https://pith.science/paper/WLGLRZBE
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · 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 v2. Results and the main claim are underlined; .

We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. result 0.71 0.96 0.93 asserted 1.00
s1 We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. method 1.00 0.88 0.04 asserted 0.99
s2 Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients. contribution 0.42 0.70 0.19 asserted 0.75

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

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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

We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients.

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