منابع مشابه
Ramification 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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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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We formulate indefinite integration with respect to an irregular functionas an algebraic problem and provide a criterion for the existence and uniqueness of asolution. This allows us to define a good notion of integral with respect to irregular pathswith Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study theproblem of the existence, uniqueness and conti...
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We are interested in (uniformly) parabolic PDEs with a nonlinear dependance of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a space-time periodic setting with a single spatial variable: ∂2u− P (a(u)∂ 1u− σ(u)f) = 0 where P is the projection on mean-zero functions, and f is a distribution and only controlled in the low regularity norm of Cα−2 for...
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We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of T. Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically invol...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2010
ISSN: 0022-0396
DOI: 10.1016/j.jde.2009.11.015