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Random bit quadrature and approximation of distributions on Hilbert Spaces

Abstract:

We study the approximation of expectations E(f(X)) for Gaussian random elements X with values in a separable Hilbert space H and Lipschitz continuous functionals f : H ! -> R. We consider restricted Monte Carlo algorithms, which may only use random bits instead of random numbers. We determine the asymptotics (in some cases sharp up to multiplicative constants, in the other cases sharp up to logarithmic factors) of the corresponding n-th minimal error in terms of the decay of the eigenvalue...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10208-018-9382-3

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hugh's College
Role:
Author
ORCID:
0000-0002-5445-3721
More from this funder
Funding agency for:
Mayer, L
Grant:
RTG 1932
Publisher:
Springer US Publisher's website
Journal:
Foundations of Computational Mathematics Journal website
Volume:
19
Issue:
1
Pages:
205–238
Publication date:
2018-03-21
Acceptance date:
2018-02-10
DOI:
EISSN:
1615-3383
ISSN:
1615-3375
Source identifiers:
824209
Keywords:
Pubs id:
pubs:824209
UUID:
uuid:3a732d95-ea9c-4135-8906-ceabde398a6e
Local pid:
pubs:824209
Deposit date:
2018-02-13

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