Pré-Publication, Document De Travail Année : 2021

Contraction criteria for Brownian filtrations samplings

Résumé

This paper investigates the problem to determine whether a given stochastic process generates a sampled Brownian filtration. A fairly general sufficient condition is obtained by applying the Frank H. Clarke contraction criteria to a functional whose construction relies on the quasi-invariance properties of a sampled Wiener measure. The latter are investigated from the precise analytic structure underlying this sampled Brownian motion. In particular, the Cameron-Martin space is identified from usual Lebesgue integrals over a Guseinov measure. As an application we obtain sufficient conditions for the existence of a solution to a class of not necessarily Markovian stochastic differential equations driven by a sampled Brownian motion. By taking a sampling times set which coincides with the unit interval, the results apply to continuous time models.

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Dates et versions

hal-04683296 , version 1 (01-09-2024)

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Rémi Lassalle. Contraction criteria for Brownian filtrations samplings. 2024. ⟨hal-04683296⟩
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