Imme Van den Berg ; Elsa Amaro - Nearly recombining processes and the calculation of expectations

arima:1907 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, September 5, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 - https://doi.org/10.46298/arima.1907
Nearly recombining processes and the calculation of expectations

Authors: Imme Van den Berg ; Elsa Amaro

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.


Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008
Published on: September 5, 2008
Submitted on: March 7, 2008
Keywords: Ito’s Lemma, expectations, near-equivalence, stroboscopy,Finite stochastic processes, recombination,Processus stochastiques finis,recombinant,presque-équivalence,espérances,Lemme d’Ito,[INFO] Computer Science [cs],[MATH] Mathematics [math]


Share

Consultation statistics

This page has been seen 90 times.
This article's PDF has been downloaded 219 times.