Flow Equations on Spaces of Rough Paths
نویسندگان
چکیده
منابع مشابه
Delay equations driven by rough paths
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متن کاملOn (p, q)-rough paths
We extend the work of T. Lyons [Lyo98] and T. Lyons and Z. Qian [LQ02] to define integrals and solutions of differential equations along product of p and q rough paths, with 1/p+1/q > 1. We use this to write an Itô formula at the level of rough paths, and to see that any rough path can always be interpreted as a product of a p-geometric rough path and a p/2-geometric rough path.
متن کاملRamification of rough paths
The stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended Chen’s multiplicative property involves the Dürr-Connes-Kreimer coproduct on rooted trees. This turns out to be the natural setting for a non-geometric theory of rough paths. MSC: 60H99; 65L99
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We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite p-variation with p ∈ [2,3) is locally Lipschitz continuous in all its arguments and we give some sufficient conditions for global existence for non-bounded vector fields.
متن کاملSensitivities via Rough Paths
Motivated by a problematic coming from mathematical finance, the paper deals with existing and additional results on the continuity and the differentiability of the Itô map associated to rough differential equations. These regularity results together with the Malliavin calculus are applied to the sensitivities analysis of stochastic differential equations driven by multidimensional Gaussian pro...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1997
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.3088