Controlled differential equations as Young integrals: A simple approach

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Lejay, Antoine

关键词: Controlled differential equations;    Young integral;    Fractional Brownian motion;    Rough paths;    Flow property;    Euler scheme;   

DOI  :  10.1016/j.jde.2010.05.006

来源: Elsevier

【 摘 要 】

The theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1 <= p < 2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by stochastic differential equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory - existence, uniqueness, convergence of the Euler scheme, flow property ... - which are spread out among several articles. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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