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On Sharp Rate of Convergence for Discretization of Integrals Driven by Fractional Brownian Motions and Related Processes with Discontinuous Integrands
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- Azmoodeh, Ehsan (författare)
- Univ Liverpool, Dept Math Sci, Liverpool, England.
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- Ilmonen, Pauliina (författare)
- Aalto Univ, Dept Math & Syst Anal, Sch Sci, Espoo, Finland.
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- Shafik, Nourhan (författare)
- Aalto Univ, Dept Math & Syst Anal, Sch Sci, Espoo, Finland.
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- Sottinen, Tommi (författare)
- Univ Vaasa, Sch Technol & Innovat, Vaasa, Finland.
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- Viitasaari, Lauri (författare)
- Uppsala universitet,Sannolikhetsteori och kombinatorik
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Univ Liverpool, Dept Math Sci, Liverpool, England Aalto Univ, Dept Math & Syst Anal, Sch Sci, Espoo, Finland. (creator_code:org_t)
- Springer, 2024
- Engelska.
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Ingår i: Journal of theoretical probability. - : Springer. - 0894-9840 .- 1572-9230. ; 37:1, s. 721-743
- Relaterad länk:
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https://doi.org/10.1...
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https://uu.diva-port... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We consider equidistant approximations of stochastic integrals driven by Hölder continuous Gaussian processes of order H > 1/2 with discontinuous integrands involving bounded variation functions. We give exact rate of convergence in the L1-distance and provide examples with different drivers. It turns out that the exact rate of convergence is proportional to n1−2H, which is twice as good as the best known results in the case of discontinuous integrands and corresponds to the known rate in the case of smooth integrands. The novelty of our approach is that, instead of using multiplicative estimates for the integrals involved, we apply a change of variables formula together with some facts on convex functions allowing us to compute expectations explicitly.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Approximation of stochastic integral
- Discontinuous integrands
- Sharp rate of convergence
- Fractional Brownian motions and related processes
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)