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Weak existence of a solution to a differential equation driven by a very rough fBm by Khoshnevisan, Davar; Swanson, Jason; Xiao, Yimin; Zhang, Liang is a scholarly article available to read on EtoBox.

What is Weak existence of a solution to a differential equation driven by a very rough fBm about?

We prove that if $f:\mathbb{R}\to\mathbb{R}$ is Lipschitz continuous, then for every $H\in(0,1/4]$ there exists a probability space on which we can construct a fractional Brownian motion $X$ with Hurst parameter $H$, together with a process $Y$ that: (i) is H\"older-continuous with H\"older exponent $\gamma$ for any $\gamma\in(0,H)$; and (ii) solves the differential equation $dY_t = f(Y_t) dX_t$. More significantly, we describe the law of the stochastic process $Y$ in terms of the solution to a non-linear stochastic partial differential equation.

Author

Khoshnevisan, Davar; Swanson, Jason; Xiao, Yimin; Zhang, Liang

Published

2013

Language

EN