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arXiv · 2312.06473

Pathwise Uniqueness for Multiplicative Young and Rough Differential Equations Driven by Fractional Brownian Motion

Toyomu Matsuda·Avi Mayorcas
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Abstract

We show pathwise uniqueness of multiplicative SDEs, in arbitrary dimensions, driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ with volatility coefficient $\sigma$ that is at least $\gamma$-H\"older continuous for $\gamma > \frac{1}{2H} \vee \frac{1-H}{H}$. This improves upon the long-standing results of [Lyo94 , Lyo98 , Dav08] which cover the same regime but require $\sigma$ to be at least $\frac{1}{H}$-H\"older continuous. Our central innovation is to combine stochastic averaging estimates with refined versions of the stochastic sewing lemma, due to [L\^e20, Ger22, MP22].

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Toyomu Matsuda, Avi Mayorcas. 2023-12-11. Pathwise Uniqueness for Multiplicative Young and Rough Differential Equations Driven by Fractional Brownian Motion. https://arxiv.org/abs/2312.06473

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