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Final Activity Report Summary - NOISEQ (Towards a general noise calculus with applications to finance science and technology)

Hyperbolic equations are known to be difficult to solve. The result from year 1 gives general conditions on the noise and on the coefficients assuring the existence of a unique solution of the corresponding Stochastic partial differential equation (SPDE). Parts of the result from year 2 are related to error calculations. The Hurst index of a fractional process is, in real world problems, always a measured, and therefore inaccurate, quantity. It is never a known, specific value given in advance by theoretical reasoning. This means that when simulating a real problem using a measured Hurst index, an error is made.

The result of year 2 gives an estimate of how big the error is. The numerical analysis shows that, when it comes to certain stochastic partial differential equations, the relation is exactly linear. This is important in technical applications.

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