Weak existence of a solution to a differential equation driven by a very rough fBm
| Autor: | Khoshnevisan, Davar, Swanson, Jason, Xiao, Yimin, Zhang, Liang |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages |
| Databáze: | arXiv |
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