Differents types de martingales a deux indices

Nualart, David

doi:10.1007/bfb0068333

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…The original need was to generalize the theory of processes à deux indices (i.e. R 2 + -indexed processes) pioneered by [10,33,35,37,42,44,45] and many others. Maybe unexpectedly, it turns out that this setting enables the study of T -indexed processes where T is quite a general partially ordered set (see Proposition 1.2 for the exact correspondance and [21] for a related approach).…”

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Hölder regularity of a Wiener integral in abstract space

Hannebicque,

Herbin

2020

Preprint

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In this article, we propose a way to consider processes indexed by a collection A of subsets of a general set T . A large class of vector spaces, manifolds and continuous R-trees are particular cases. Lattice-theoretic and topological assumptions are considered separately with a view to clarifying the exposition. We then define a Wiener-type integral YA = A f dX for all A ∈ A for a deterministic function f : T → R and a set-indexed Lévy process X. It is a particular case of Raput and Rosinski [40], but our setting enables a quicker construction and yields more properties about the sample paths of Y. Finally, bounds for the Hölder regularity of Y are given which indicate how the regularities of f and X contributes to that of Y . This follows the works of Jaffard [24] and Balança and Herbin [6].

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