Intégrales stochastiques de processus anticipants et projections duales prévisibles

• Autores: Marc Yor, C. Donati-Martin
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 43, Nº 1, 1999, págs. 281-301
• Idioma: francés
• DOI: 10.5565/publmat_43199_13
• Títulos paralelos:
  • Integrales estocásticas de procesos anticipantes y proyecciones duales previsibles
  • Stochastic integrals of anticipating processes and dual predictable projections
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• Resumen

  • We define a stochastic anticipating integral $\delta^\mu$ with respect to Brownian motion, associated to a non adapted increasing process $(\mu_t)$, with dual projection $t$. The integral $\delta^\mu (u) $ of an anticipating process $(u_t)$ satisfies: for every bounded predictable process $f_t$, $$ E\left[\left(\int f_s\, dB_s\right) \delta^\mu (u)\right ] = E\left[ \int f_s u_s \, d\mu_s\right].

    $$ We characterize this integral when $\mu_t = \sup_{t \leq s \leq 1} B_s$. The proof relies on a path decomposition of Brownian motion up to time 1.