Titlebook: Séminaire de Probabilités XLV; Catherine Donati-Martin,Antoine Lejay,Alain Rouaul Book 2013 Springer International Publishing Switzerland

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Vershik’s Intermediate Level Standardness Criterion and the Scale of an Automorphismim to provide an easily applicable probabilistic statement of this criterion. Finally, Vershik’s intermediate level criterion is illustrated by revisiting Vershik’s definition of the scale of an invertible measure-preserving transformation.

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Functional Co-monotony of Processes with Applications to Peacocks and Barrier Optionsby a former work of Carr et al. in (Finance Res. Lett. 5:162–171, 2008) about the sensitivities of Asian options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.

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Book 2013o the September 2011 Conference on Stochastic Filtrations, held in Strasbourg and organized by Michel Émery, have also contributed to the present volume. The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.

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Some Sufficient Conditions for the Ergodicity of the Lévy Transformationthe Lévy transformation of the Wiener-space is ergodic. Our main results are formulated in terms of a strongly stationary sequence of random variables obtained by evaluating the iterated paths at time one. Roughly speaking, this sequence has to approach zero “sufficiently fast”. For example, one of

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Vershik’s Intermediate Level Standardness Criterion and the Scale of an Automorphism This criterion, whose nature is combinatorial, has been intensively used in the ergodic-theoretic literature, but it is not easily applicable by probabilists because it is stated in a language specific to the theory of measurable partitions and has not been translated into probabilistic terms. We a

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Characterising Ocone Local Martingales with Reflectionsof positive real numbers converging to 0 such that . satisfies the reflection principle at levels 0, .. and 2.., for each . ≥ 1, then . is an Ocone local martingale. They also asked whether the reflection principle at levels 0 and .. only (for each . ≥ 1) is sufficient to ensure that . is an Ocone l