Synchronization by noise for stochastic differential equations driven by fractional Brownian motion
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918386647171072 |
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| author | Blessing, Alexandra Varzaneh, Mazyar Ghani |
| author_facet | Blessing, Alexandra Varzaneh, Mazyar Ghani |
| contents | We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak form of synchronization occurs. To this aim we use tools from stochastic dynamical systems, random dynamical systems and a support theorem for SDEs driven by fractional noise.~In particular, we characterize the support of an invariant measure of a random dynamical system in a non-Markovian setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12774 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Synchronization by noise for stochastic differential equations driven by fractional Brownian motion Blessing, Alexandra Varzaneh, Mazyar Ghani Probability Dynamical Systems 60G22, 60F99, 37H30 We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak form of synchronization occurs. To this aim we use tools from stochastic dynamical systems, random dynamical systems and a support theorem for SDEs driven by fractional noise.~In particular, we characterize the support of an invariant measure of a random dynamical system in a non-Markovian setting. |
| title | Synchronization by noise for stochastic differential equations driven by fractional Brownian motion |
| topic | Probability Dynamical Systems 60G22, 60F99, 37H30 |
| url | https://arxiv.org/abs/2603.12774 |