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Displaying similar documents to “Smoothness of Itô maps and diffusion processes on path spaces (I)”

Differential equations driven by rough signals.

Terry J. Lyons (1998)

Revista Matemática Iberoamericana

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This paper aims to provide a systematic approach to the treatment of differential equations of the type dyt = Σi fi(yt) dxt i where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued...

Path-wise solutions of stochastic differential equations driven by Lévy processes.

David R. E. Williams (2001)

Revista Matemática Iberoamericana

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In this paper we show that a path-wise solution to the following integral equation Yt = ∫0 t  f(Yt) dXt,     Y0 = a ∈ Rd, exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α >...