A Girsanov Result through Birkhoff Integral

Abstract

A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by substitution, in order to fix the measure-theoretic tools needed for the main result, Theorem 6, where a martingale equivalent to the underlying vector probability has been obtained in order to represent the modified process as a martingale with the same marginals as the original one.

References in corpus (8)

• Gauge integrals and selections of weakly compact valued multifunctions
• An extension of the Birkhoff integrability for multifunctions
• Relations among Gauge and Pettis integrals for $cwk(X)$-valued multifunctions
• Some new results on integration for multifunction
• Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures
• A note on comparison between Birkhoff and McShane-type integrals for multifunctions
• Order-type Henstock and McShane integrals in Banach lattice setting
• Set-valued Brownian motion

Cited by in corpus (1)

• A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability