Nearly recombining processes and the calculation of expectations

• Autor(a) principal: van den Berg, Imme
• Data de Publicação: 2008
• Outros Autores: Amaro, Elsa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/1395
• topic: Discrete stochastic processes; recombination; near-equivalence; stroboscopy; expectations; Ito's Lemma

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.