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Distribution functions of Poisson random integrals: Analysis and computation

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Mark S. Veillette, Murad S. Taqqu

Probability · Submitted 29 Apr 2010

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

The authors' main claim We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples.

how it is stated · asserted 1.00 read the record →

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arXiv ID1004.5338 (version 1)
Pith IDGRFV5UIB, Pith's permanent record of this paper and its review
CitationMark S. Veillette, Murad S. Taqqu. "Distribution functions of Poisson random integrals: Analysis and computation." arXiv:1004.5338 (2010). https://pith.science/paper/GRFV5UIB
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,629 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.08 · mentions code or data availability 0.95.

The abstract, sentence by sentence

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

We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral $I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds)$, where $N$ is a Poisson random measure with control measure $n$ and $\krnl$ is a suitable kernel function. We do so by combining a Kolmogorov-Feller equation with a finite-difference scheme. We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. The software used to implement the procedure is available on demand and we demonstrate its use in the paper.

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 We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral $I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds)$, where $N$ is a Poisson random measure with control measure $n$ and $\krnl$ is a suitable kernel function. background 0.70 0.25 0.06 asserted 0.80
s1 We do so by combining a Kolmogorov-Feller equation with a finite-difference scheme. method 1.00 0.91 0.09 asserted 1.00
s2 We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. contribution 0.83 0.95 0.28 asserted 1.00
s3 The software used to implement the procedure is available on demand and we demonstrate its use in the paper. contribution 0.61 0.81 0.04 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.91.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • 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

We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral $I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds)$, where $N$ is a Poisson random measure with control measure $n$ and $\krnl$ is a suitable kernel function. We do so by combining a Kolmogorov-Feller equation with a finite-difference scheme. We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. The software used to implement the procedure is available on demand and we demonstrate its use in the paper.

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