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Displaying similar documents to “A Non-Central Functional Limit Theorem for Quadratic Forms in Martingale Difference Sequences”

Théorèmes limites avec poids pour les martingales vectorielles

Faouzi Chaabane, Faïza Maaouia (2010)

ESAIM: Probability and Statistics

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We give limit theorems specifying weak and strong rates of convergence associated to a quadratic extension of the martingale almost-sure central limit theorem. Some typical examples are discussed to illustrate how to make use of them in statistic.

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

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In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.