منابع مشابه
Non-linear rough heat equations
This article is devoted to define and solve an evolution equation of the form dyt = yt dt + d Xt (yt ), where stands for the Laplace operator on a space of the form L p(Rn), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt (φ) = ∑N i=1 xi t fi (φ), where each x = (x (1), . . . , x (N ) is a γ -Hölder function generating a rough path and each fi is a smooth enou...
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This article is devoted to define and solve an evolution equation of the form dyt = ∆yt dt + dXt(yt), where ∆ stands for the Laplace operator on a space of the form L(R), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt(φ) = ∑N i=1 x i tfi(φ), where each x = (x , . . . , x) is a γ-Hölder function generating a rough path and each fi is a smooth enough function d...
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We study linear rough differential equations and we solve perturbed linear rough differential equation using the Duhamel principle. These results provide us with the key technical point to study the regularity of the differential of the Itô map in a subsequent article. Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach alge...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2011
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-011-0341-z