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A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion.

Baker, David, Yor, Marc (2009)

Electronic Journal of Probability [electronic only]

A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.

Zemlys, Vaidotas (2008)

Electronic Journal of Probability [electronic only]

A limit theorem for the prediction process under absolute continuity

Hideatsu Tsukahara (1999)

Séminaire de probabilités de Strasbourg

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, $ℱ$ , ( $ℱ_{t}$ )t≥0, $ℙ$ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to $ℱ_{\infty}$ (theσ-algebra generated by ( $ℱ_{t}$ )t≥0) a coherent family of probability measures ( $ℚ_{t}$ ) indexed byt≥0, each of them being defined on $ℱ_{t}$ . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, $ℱ$ , ( $ℱ_{t}$ )t≥0, $ℙ$ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to $ℱ_{\infty}$ (the σ-algebra generated by ( $ℱ_{t}$ )t≥0) a coherent family of probability measures ( $ℚ_{t}$ ) indexed by t≥0, each of them being defined on $ℱ_{t}$ . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...