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Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem
- Publication Year :
- 2018
- Publisher :
- HAL CCSD, 2018.
-
Abstract
- Consider the multivariate Stein equation $\Delta f - x\cdot \nabla f = h(x) - E h(Z)$, where $Z$ is a standard $d$-dimensional Gaussian random vector, and let $f\_h$ be the solution given by Barbour's generator approach. We prove that, when $h$ is $\alpha$-H\"older ($0
- Subjects :
- Probability (math.PR)
Mathematics - Statistics Theory
Statistics Theory (math.ST)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
Mathematics - Analysis of PDEs
Mathematics::Probability
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
FOS: Mathematics
AMS subjects classification. 60F05, 35B65, 35J15
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Stein's method
[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]
[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Berry-esseen bounds
Mathematics - Probability
Analysis of PDEs (math.AP)
Elliptic regularity
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a209d57badf7ceb31096cbf4dd36c1f8