Conditional stochastic differential equations driven by fractional Brownian motion
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910246869401600 |
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| author | Đorđević, Jasmina Øksendal, Bernt |
| author_facet | Đorđević, Jasmina Øksendal, Bernt |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08324 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditional stochastic differential equations driven by fractional Brownian motion Đorđević, Jasmina Øksendal, Bernt Probability Functional Analysis 60H35, 93E10, 93E25 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. |
| title | Conditional stochastic differential equations driven by fractional Brownian motion |
| topic | Probability Functional Analysis 60H35, 93E10, 93E25 |
| url | https://arxiv.org/abs/2306.08324 |