Titlebook: Seminaire de Probabilites XXXIII; Jacques Azéma,Michel Émery,Marc Yor Conference proceedings 1999 Springer-Verlag Berlin Heidelberg 1999 B

苦笑

A bipolar theorem for ,,quals its closed convex hull..The space . of real-valued random variables on a probability space . equipped with the topology of convergence in measure fails to be locally convex so that—a priori—the classical bipolar theorem does not apply. In this note we show an analogue of the bipolar theorem fo

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终点

A stochastic differential equation with a unique (up to indistinguishability) but not strong solutin motion and for any initial value, SDE (1) has at most one (weak) solution. We present an example that if we only assume that, for any initial value, there is at most one solution process on the . space (Ω,..).,P), we can no longer conclude that the solution . is strong.

抛物线

Dynamics of stochastic approximation algorithms,These notes were written for a D.E.A. course given at . de Cachan during the 1996–97 and 1997–98 academic years and at . during the 1997–98 academic year. Their aim is to introduce the reader to the dynamical system aspects of the theory of stochastic approximations.

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On the joining of sticky brownian motion,We present an example of a one-dimensional diffusion that cannot be innovated by Brownian motion. We do this by studying the ways in which two copies of sticky Brownian motion may be joined together and applying Tsirel‘son‘s criteria of cosiness.

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A short proof of decomposition of strongly reduced martingales,A short proof of the following theorem is given: If . is a martingale, .>0 is a stopping time, .. and . is bounded, then . is a sum of a . (and, thus, square-integrable) martingale and a martingale of integrable variation.

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Jacques Azéma,Michel Émery,Marc YorIncludes supplementary material:

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