Multi-level Monte Carlo approximation of distribution functions and densities
We construct and analyze multi-level Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable a...
| Main Authors: | , , |
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2015
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| _version_ | 1826297901183139840 |
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| author | Giles, M Nagapetyan, T Ritter, K |
| author_facet | Giles, M Nagapetyan, T Ritter, K |
| author_sort | Giles, M |
| collection | OXFORD |
| description | We construct and analyze multi-level Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable assumptions on the weak and strong convergence. We apply the results to smooth path-independent and path-dependent functionals and to stopped exit times of SDEs. |
| first_indexed | 2024-03-07T04:38:41Z |
| format | Journal article |
| id | oxford-uuid:d0dd57ee-5116-4e79-ba71-f47c55075598 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:38:41Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:d0dd57ee-5116-4e79-ba71-f47c550755982022-03-27T07:53:02ZMulti-level Monte Carlo approximation of distribution functions and densitiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d0dd57ee-5116-4e79-ba71-f47c55075598Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2015Giles, MNagapetyan, TRitter, KWe construct and analyze multi-level Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable assumptions on the weak and strong convergence. We apply the results to smooth path-independent and path-dependent functionals and to stopped exit times of SDEs. |
| spellingShingle | Giles, M Nagapetyan, T Ritter, K Multi-level Monte Carlo approximation of distribution functions and densities |
| title | Multi-level Monte Carlo approximation of distribution functions and densities |
| title_full | Multi-level Monte Carlo approximation of distribution functions and densities |
| title_fullStr | Multi-level Monte Carlo approximation of distribution functions and densities |
| title_full_unstemmed | Multi-level Monte Carlo approximation of distribution functions and densities |
| title_short | Multi-level Monte Carlo approximation of distribution functions and densities |
| title_sort | multi level monte carlo approximation of distribution functions and densities |
| work_keys_str_mv | AT gilesm multilevelmontecarloapproximationofdistributionfunctionsanddensities AT nagapetyant multilevelmontecarloapproximationofdistributionfunctionsanddensities AT ritterk multilevelmontecarloapproximationofdistributionfunctionsanddensities |