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Ordinary differential equations with fractal noise |
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| Authors: | F. Klingenhö fer M. Zä hle |
| Affiliation: | Mathematical Institute, University of Jena, D-07740 Jena, Germany ; Mathematical Institute, University of Jena, D-07740 Jena, Germany |
| Abstract: | The differential equation
for fractal-type functions |
| Keywords: | |
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is determined via fractional calculus. Under appropriate conditions we prove existence and uniqueness of a local solution by means of its representation 
for certain 
-functions 
and 
. The method is also applied to Itô stochastic differential equations and leads to a general pathwise representation. Finally we discuss fractal sample path properties of the solutions.