Weak solutions for stochastic differential equations with additive fractional noise

Pedro J. Catuogno; Diego S. Ledesma

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arXiv · 2206.07159

Weak solutions for stochastic differential equations with additive fractional noise

Pedro J. Catuogno·Diego S. Ledesma

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Abstract

We give a new approach to prove the existence of a weak solution of \[dx_t = f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property of the fractional Brownian motion in order to obtain a weak solution for this equation.

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Pedro J. Catuogno, Diego S. Ledesma. 2022-06-14. Weak solutions for stochastic differential equations with additive fractional noise. https://arxiv.org/abs/2206.07159

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