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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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Submitted on : Tuesday, February 23, 2016 - 11:13:05 AM
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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, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008, pp.389-417. ⟨10.46298/arima.1907⟩. ⟨hal-01277782⟩

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