MLMC for nested expectations
This paper discusses progress and future research possibilities in applying MLMC ideas to nested expectations of the form 𝔼[𝑔(𝔼[𝑓(𝑋,𝑌)|𝑋])], with an outer expectation with respect to one random variable X, and an inner conditional expectation with respect to a second random variable Y . The difficul...
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| Format: | Book section |
| Language: | English |
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Springer
2018
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| _version_ | 1797107121673732096 |
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| author | Giles, MB |
| author2 | Dick, J |
| author_facet | Dick, J Giles, MB |
| author_sort | Giles, MB |
| collection | OXFORD |
| description | This paper discusses progress and future research possibilities in applying MLMC ideas to nested expectations of the form 𝔼[𝑔(𝔼[𝑓(𝑋,𝑌)|𝑋])], with an outer expectation with respect to one random variable X, and an inner conditional expectation with respect to a second random variable Y . The difficulty in treating such applications is shown to depend on whether the function g is (1) smooth, (2) continuous and piecewise smooth, or (3) discontinuous. |
| first_indexed | 2024-03-07T07:11:58Z |
| format | Book section |
| id | oxford-uuid:316e03f0-e441-4c3a-a885-164604be3fa6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:11:58Z |
| publishDate | 2018 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:316e03f0-e441-4c3a-a885-164604be3fa62022-06-30T15:25:05ZMLMC for nested expectationsBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:316e03f0-e441-4c3a-a885-164604be3fa6EnglishSymplectic Elements at OxfordSpringer2018Giles, MBDick, JKuo, FYWozniakowski, HThis paper discusses progress and future research possibilities in applying MLMC ideas to nested expectations of the form 𝔼[𝑔(𝔼[𝑓(𝑋,𝑌)|𝑋])], with an outer expectation with respect to one random variable X, and an inner conditional expectation with respect to a second random variable Y . The difficulty in treating such applications is shown to depend on whether the function g is (1) smooth, (2) continuous and piecewise smooth, or (3) discontinuous. |
| spellingShingle | Giles, MB MLMC for nested expectations |
| title | MLMC for nested expectations |
| title_full | MLMC for nested expectations |
| title_fullStr | MLMC for nested expectations |
| title_full_unstemmed | MLMC for nested expectations |
| title_short | MLMC for nested expectations |
| title_sort | mlmc for nested expectations |
| work_keys_str_mv | AT gilesmb mlmcfornestedexpectations |