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- W4293497555 abstract "Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a Holder continuous function with Holder exponent in $(1/3,1/2)$. Our stochastic integral is in some sense a generalization of the well-known Young integral and can be defined independently of the initial condition. Similar to the Rough Path Theory we establish a second variable which is given, roughly speaking, by a tensor product. It is then necessary to formulate a second equation for this new variable, and we do in a mild sense. The crucial point in order to get this new equation is to construct a tensor depending on the noise path but also on the semigroup. We then prove the existence of a unique Holder continuous solution of the system of equations, consisting of the path and the area components, if the nonlinear term and the initial condition are sufficiently smooth. Once the abstract theory is developed, we can present a pathwise nonlinear SPDE driven by a fractional Brownian motion with Hurst parameter in $(1/3,1/2]$." @default.
- W4293497555 created "2022-08-29" @default.
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- W4293497555 date "2012-05-30" @default.
- W4293497555 modified "2023-10-18" @default.
- W4293497555 title "Pathwise solutions to stochastic partial differential equations driven by fractional Brownian motions with Hurst parameters in $(1/3,1/2]$" @default.
- W4293497555 doi "https://doi.org/10.48550/arxiv.1205.6735" @default.
- W4293497555 hasPublicationYear "2012" @default.
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