 Euler scheme for SDEs driven by fractional Brownian motions: Malliavin differentiability and uniform upper-bound estimatesJorge A. León, Yanghui Liu and Samy Tindel Stochastic Processes and their Applications, 2024, vol. 175, issue C Abstract: The Malliavin differentiability of a SDE plays a crucial role in the study of density smoothness and ergodicity among others. For Gaussian driven SDEs the differentiability issue is solved essentially in Cass et al., (2013). In this paper, we consider the Malliavin differentiability for the Euler scheme of such SDEs. We will focus on SDEs driven by fractional Brownian motions (fBm), which is a very natural class of Gaussian processes. We derive a uniform (in the step size n) path-wise upper-bound estimate for the Euler scheme for stochastic differential equations driven by fBm with Hurst parameter H>1/3 and its Malliavin derivatives. Keywords: Rough paths; Discrete sewing lemma; Fractional Brownian motion; Stochastic differential equations; Euler scheme; Asymptotic error distributions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:175:y:2024:i:c:s0304414924001182 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104412 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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