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Pré-Publication, Document De Travail Année : 2015

Convergence rate of strong approximations of compound random maps

Résumé

We consider a random map x → F (ω, x) and a random variable Θ(ω), and we denote by F^N (ω, x) and Θ^N (ω) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation F^N (ω, Θ^N (ω)) to the compound variable F (ω, Θ(ω)), in terms of the approximations of F and Θ. Two applications of this result are then developed: Firstly, composition of two Stochastic Differential Equations through their initial conditions; secondly, approximation of stochastic processes (possibly non semi-martingales) at random times (possibly non stopping times).
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Dates et versions

hal-01141320 , version 1 (11-04-2015)
hal-01141320 , version 2 (27-04-2016)

Identifiants

  • HAL Id : hal-01141320 , version 1

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Emmanuel Gobet, Mohamed Mrad. Convergence rate of strong approximations of compound random maps. 2015. ⟨hal-01141320v1⟩
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