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Embedding of random vectors into continuous martingales

E. Dettweiler (1999)

Studia Mathematica

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 Ω ˜ of Ω, and a filtration ( ˜ t ) t 0 on Ω ˜ , such that for every X L 0 ( Ω , E ) there is an E-valued, continuous ( ˜ t ) -martingale ( M t ( X ) ) t 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 L 0 ( Ω , ) , and for general E this leads to a representation of random vectors as...

Empirical estimates in stochastic optimization via distribution tails

Vlasta Kaňková (2010)

Kybernetika

“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied mostly for...

Enhanced Gaussian processes and applications

Laure Coutin, Nicolas Victoir (2009)

ESAIM: Probability and Statistics

We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.

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