Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation | Zendy

A. M. Davie | Zendy

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Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation

Author(s) -

A. M. Davie

Publication year - 2008

Publication title -

applied mathematics research express

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.763

H-Index - 20

eISSN - 1687-1200

pISSN - 1687-1197

DOI - 10.1093/amrx/abm009

Subject(s) - stochastic differential equation , brownian motion , mathematics , differential equation , path (computing) , euler's formula , differential (mechanical device) , mathematical analysis , motion (physics) , computer science , classical mechanics , physics , statistics , thermodynamics , programming language

driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.

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