The approximate Euler method for Lévy driven stochastic differential equations
Jean Jacod, Thomas G. Kurtz, Sylvie Méléard, Philip Protter (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Displaying similar documents to “Anticipative calculus with respect to filtered Poisson processes”
The approximate Euler method for Lévy driven stochastic differential equations
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We define a class of distributions on Poisson space which allows to iterate a modification of the gradient of [1]. As an application we obtain, with relatively short calculations, a formula for the chaos expansion of functionals of jump times of the Poisson process.
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A stochastic min-driven coalescence process and its hydrodynamical limit
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A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalized version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.