Numerical Schemes for Rough Parabolic Equations

Journal Article · Sun Apr 15 00:00:00 EDT 2012 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-011-9157-6· OSTI ID:22043789

Deya, Aurelien ^[1]

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1. Universite de Nancy 1, Institut Elie Cartan Nancy (France)

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.

• OSTI ID: 22043789
• Journal Information: Applied Mathematics and Optimization, Vol. 65, Issue 2; Other Information: Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
BROWNIAN MOVEMENT
GEOMETRY
INDEXES
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES