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Smoothness of Ito maps and diffusion processes on path spaces

Abstract:

Let p ∈ [1, 2) and α, ε > 0 be such that α ∈ (p - 1, 1 - ε). Let V, W be two Euclidean spaces. Let Ωp (V) be the space of continuous paths taking values in V and with finite p-variation. Let k ∈ N and f : W → Hom (V, W) be a Lip (k + α + ε) map in the sense of E.M. Stein [Stein E.M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970]. In this paper we prove that the Itô map, defined by I...

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Publication status:
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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
Volume:
39
Issue:
4
Pages:
649-677
Publication date:
2006-01-01
DOI:
ISSN:
0012-9593
Source identifiers:
20384
Language:
English
Pubs id:
pubs:20384
UUID:
uuid:8bba1dbc-e38a-41fd-bb67-25ef3c29f6df
Local pid:
pubs:20384
Deposit date:
2012-12-19

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