Embedding of random vectors into continuous martingales
Let E be a real, separable Banach space and denote by the space of all E-valued random vectors defined on the probability space Ω. The following result is proved. There exists an extension of Ω, and a filtration on , such that for every there is an E-valued, continuous -martingale in which X is embedded in the sense that a.s. for an a.s. finite stopping time τ. For E = ℝ this gives a Skorokhod embedding for all , and for general E this leads to a representation of random vectors as...