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Nearly recombining processes and the calculation of expectations

Abstract : In the context of Nonstandard Analysis, we study stochastic difference equations with infinitesimal time-steps. In particular we give a necessary and sufficient condition for a solution to be nearly-equivalent to a recombining stochastic process. The characterization is based upon a partial differential equation involving the trend and the conditional variance of the original process. An analogy with Ito’s Lemma is pointed out. As an application we obtain a method for approximation of expectations, in terms of two ordinary differential equations, also involving the trend and the conditional variance of the original process, and of Gaussian integrals.
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https://hal.inria.fr/hal-01277782
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Imme van den Berg, Elsa Amaro. Nearly recombining processes and the calculation of expectations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, 9, pp.389-417. ⟨hal-01277782⟩

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