An adaptive random bit multilevel algorithm for SDEs
We study the approximation of expectations E(f (X)) for solutions X of stochastic differential equations and functionals f on the path space by means of Monte Carlo algorithms that only use random bits instead of random numbers. We construct an adaptive random bit multilevel algorithm, which is base...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Book section |
| Language: | English |
| Published: |
De Gruyter
2020
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| _version_ | 1826311108315578368 |
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| author | Giles, MB Hefter, M Mayer, L Ritter, K |
| author2 | Hickernell, FJ |
| author_facet | Hickernell, FJ Giles, MB Hefter, M Mayer, L Ritter, K |
| author_sort | Giles, MB |
| collection | OXFORD |
| description | We study the approximation of expectations E(f (X)) for solutions X of stochastic differential equations and functionals f on the path space by means of Monte Carlo algorithms that only use random bits instead of random numbers. We construct an adaptive random bit multilevel algorithm, which is based on the Euler scheme, the Lévy-Ciesielski representation of the Brownian motion, and asymptotically optimal random bit approximations of the standard normal distribution. We numerically compare this algorithm with the adaptive classical multilevel Euler algorithm for a geometric Brownian motion, an Ornstein-Uhlenbeck process, and a Cox-Ingersoll-Ross process. |
| first_indexed | 2024-03-07T08:03:30Z |
| format | Book section |
| id | oxford-uuid:5b7116c6-d52b-42b6-a910-517d9131e0c4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:03:30Z |
| publishDate | 2020 |
| publisher | De Gruyter |
| record_format | dspace |
| spelling | oxford-uuid:5b7116c6-d52b-42b6-a910-517d9131e0c42023-10-17T10:49:32ZAn adaptive random bit multilevel algorithm for SDEsBook sectionhttp://purl.org/coar/resource_type/c_1843uuid:5b7116c6-d52b-42b6-a910-517d9131e0c4EnglishSymplectic ElementsDe Gruyter2020Giles, MBHefter, MMayer, LRitter, KHickernell, FJKritzer, PWe study the approximation of expectations E(f (X)) for solutions X of stochastic differential equations and functionals f on the path space by means of Monte Carlo algorithms that only use random bits instead of random numbers. We construct an adaptive random bit multilevel algorithm, which is based on the Euler scheme, the Lévy-Ciesielski representation of the Brownian motion, and asymptotically optimal random bit approximations of the standard normal distribution. We numerically compare this algorithm with the adaptive classical multilevel Euler algorithm for a geometric Brownian motion, an Ornstein-Uhlenbeck process, and a Cox-Ingersoll-Ross process. |
| spellingShingle | Giles, MB Hefter, M Mayer, L Ritter, K An adaptive random bit multilevel algorithm for SDEs |
| title | An adaptive random bit multilevel algorithm for SDEs |
| title_full | An adaptive random bit multilevel algorithm for SDEs |
| title_fullStr | An adaptive random bit multilevel algorithm for SDEs |
| title_full_unstemmed | An adaptive random bit multilevel algorithm for SDEs |
| title_short | An adaptive random bit multilevel algorithm for SDEs |
| title_sort | adaptive random bit multilevel algorithm for sdes |
| work_keys_str_mv | AT gilesmb anadaptiverandombitmultilevelalgorithmforsdes AT hefterm anadaptiverandombitmultilevelalgorithmforsdes AT mayerl anadaptiverandombitmultilevelalgorithmforsdes AT ritterk anadaptiverandombitmultilevelalgorithmforsdes AT gilesmb adaptiverandombitmultilevelalgorithmforsdes AT hefterm adaptiverandombitmultilevelalgorithmforsdes AT mayerl adaptiverandombitmultilevelalgorithmforsdes AT ritterk adaptiverandombitmultilevelalgorithmforsdes |