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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...

Ergodicity of a certain class of non Feller models : applications to 𝐴𝑅𝐶𝐻 and Markov switching models

Jean-Gabriel Attali (2004)

ESAIM: Probability and Statistics

We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.

Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models

Jean-Gabriel Attali (2010)

ESAIM: Probability and Statistics

We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.

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