Stochastic differential equations 
driven by processes generated by divergence form 
operators II: convergence results

Antoine Lejay

Displaying similar documents to “Stochastic differential equations driven by processes generated by divergence form operators II: convergence results”

Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem

Antoine Lejay (2006)

ESAIM: Probability and Statistics

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We show in this article how the theory of “rough paths” allows us to construct solutions of differential equations (SDEs) driven by processes generated by divergence-form operators. For that, we use approximations of the trajectories of the stochastic process by piecewise smooth paths. A result of type Wong-Zakai follows immediately.

On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.

Lejay, Antoine (2002)

Electronic Journal of Probability [electronic only]

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Comparison results for reflected jump-diffusions in the orthant with variable reflection directions and stability applications.

Piera, Francisco J., Mazumdar, Ravi R. (2008)

Electronic Journal of Probability [electronic only]

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Asymptotic properties of power variations of Lévy processes

Jean Jacod (2007)

ESAIM: Probability and Statistics

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We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function evaluated at the increments of a Lévy process between the successive times Δ for = 0,1,...,. One can elucidate completely the first order behavior, that is the convergence in probability of such sums, possibly after normalization and/or centering: it turns out that there is a rather wide variety of possible behaviors, depending on the structure of jumps and on the...