Abstract:The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with $H>\tfrac{1}{2}$. For this, we summarise the theory of fractional white noise and prove a fundamental $L^2$-estimate for WIS-integrals. We apply this to prove the existence and uniqueness of a solution in $L^2(P)$ of a conditional WIS-stochastic differential equation driven by a fractional Brownian motion with $H>\tfrac{1}{2}$ under Lipschitz conditions on its coefficients.
| Subjects: | Probability (math.PR); Functional Analysis (math.FA) |
| MSC classes: | 60H35, 93E10, 93E25 |
| Cite as: | arXiv:2306.08324 [math.PR] |
| (or arXiv:2306.08324v4 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2306.08324 arXiv-issued DOI via DataCite |
From: Bernt Øksendal [view email]
[v1]
Wed, 14 Jun 2023 07:53:19 UTC (13 KB)
[v2]
Fri, 15 Sep 2023 09:17:19 UTC (14 KB)
[v3]
Fri, 16 Aug 2024 08:27:14 UTC (17 KB)
[v4]
Fri, 22 May 2026 07:59:52 UTC (19 KB)
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