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Optimal approximation of anticipating SDEs

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Peter Parczewski

Probability · Submitted 28 Mar 2019

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

The authors' main claim We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense.

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arXiv ID1903.12034 (version 2)
Pith ID3ZKU4GKG, Pith's permanent record of this paper and its review
CitationPeter Parczewski. "Optimal approximation of anticipating SDEs." arXiv:1903.12034 (2019). https://pith.science/paper/3ZKU4GKG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,954 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.86 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. Although alternative proof techniques are needed, our results can be seen as generalizations of the corresponding results for It\=o SDEs. As a key tool we extend optimal approximation results for vectors of correlated Wiener integrals to general random vectors, which contain the solutions of our Skorohod SDEs.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. result 0.64 0.96 0.89 asserted 1.00
s1 Although alternative proof techniques are needed, our results can be seen as generalizations of the corresponding results for It\=o SDEs. interpretation 0.99 0.48 0.07 hedged possibility 0.50
s2 As a key tool we extend optimal approximation results for vectors of correlated Wiener integrals to general random vectors, which contain the solutions of our Skorohod SDEs. method 0.90 0.90 0.08 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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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 derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. Although alternative proof techniques are needed, our results can be seen as generalizations of the corresponding results for It\=o SDEs. As a key tool we extend optimal approximation results for vectors of correlated Wiener integrals to general random vectors, which contain the solutions of our Skorohod SDEs.

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