Abstract
We prove the strong law of large numbers for random signed measures. The result is uniform over a family of subsets under mild assumptions.
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Based on a talk at the conference Stereology, Spatial Statistics, and Stochastic Geometry in Prague, June 25–29, 2018.
Supported by the grant 0118U003614 from Ministry of Education and Science of Ukraine (project N2105Φ).
Supported by the grant 0118U003614 from Ministry of Education and Science of Ukraine (project N2105Φ) and by the grant IZ7320_152292 from Swiss National Science Foundation.
Supported by the grant IZ7320_152292 from Swiss National Science Foundation.
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Bogdanskii, V.Y., Klesov, O.I. & Molchanov, I. Uniform Strong Law of Large Numbers. Methodol Comput Appl Probab 23, 461–470 (2021). https://doi.org/10.1007/s11009-019-09711-x
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DOI: https://doi.org/10.1007/s11009-019-09711-x
Keywords
- Random signed measure
- Strong law of large numbers
- Uniform limit theorem over a family of subsets
- Partial sum stochastic processes