EUDML

Let E be a real, separable Banach space and denote by $L^{0} (Ω, E)$ the space of all E-valued random vectors defined on the probability space Ω. The following result is proved. There exists an extension $\tilde{Ω}$ of Ω, and a filtration ${({\tilde{ℱ}}_{t})}_{t \geq 0}$ on $\tilde{Ω}$ , such that for every $X \in L^{0} (Ω, E)$ there is an E-valued, continuous $({\tilde{ℱ}}_{t})$ -martingale ${(M_{t} (X))}_{t \geq 0}$ in which X is embedded in the sense that $X = M_{τ} (X)$ a.s. for an a.s. finite stopping time τ. For E = ℝ this gives a Skorokhod embedding for all $X \in L^{0} (Ω, ℝ)$ , and for general E this leads to a representation of random vectors as...

Infinitely divisible measures on the cone of an ordered locally convex vector spaces

E. Dettweiler — 1976

Annales scientifiques de l'Université de Clermont. Mathématiques

Continuous factorizations of covariance operators and Gaussian processes

G. Little; E. Dettweiler — 1987

Studia Mathematica

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Stationary Random Processes Associated with Point Processes - Rolski, T.

Parameterschätzung von Eingleichungsmodellen im unbeschränkten Parameterraum - Kuhlmann, W.

Über die Existenz überall trennscharfer Tests im nicht-dominierten Fall.

A Course in Large Sample Theory - T. S. Ferguson.

Probability with a View Toward Statistics, Vol. I + II - J. Hoffmann-Jorgensen.

Embedding of random vectors into continuous martingales

Infinitely divisible measures on the cone of an ordered locally convex vector spaces

Continuous factorizations of covariance operators and Gaussian processes