Controlled differential equations as Young integrals: A simple approach |
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Authors: | Antoine Lejay |
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Institution: | Institut Elie Cartan Nancy Université, CNRS, INRIA, Boulevard des Aiguillettes, B.P. 239, F-54506 Vandœuvre-lès-Nancy, France |
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Abstract: | 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. |
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Keywords: | Controlled differential equations Young integral Fractional Brownian motion Rough paths Flow property Euler scheme |
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