Numerical Schemes for Rough Parabolic Equations

Numerical Schemes for Rough Parabolic Equations This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489–1518, 2011 ) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H >1/3. Applied Mathematics and Optimization Springer Journals

Numerical Schemes for Rough Parabolic Equations

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Copyright © 2012 by Springer Science+Business Media, LLC
Mathematics; Numerical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
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