Autour d'un théorème de tsirelson sur des filtrations Browniennes et non Browniennes

Barlow, Martin T.; Émery, Michel; Knight, Frank B.; Song, Sang-Keun; Yor, Marc

doi:10.1007/bfb0101763

Cited by 61 publications

(68 citation statements)

References 14 publications

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“…For the sake of convenience, we assume that γ in the decomposition (1) given by the stochastic self-contractivity assumption (2), is the Lebesgue measure on [0, 1]. Moreover we write f (x, u) instead of ∇ u (x).…”

Section: Example 350 (Stationary Markov Chain On a Denumerable Space)mentioning

confidence: 99%

“…The classical definition of an embedding between from a probability space (Ω, B, P) into a probability space (Ω ′ , A ′ , P ′ ) is given in terms of a Boolean morphism from B/P into A ′ /P which preserves probabilities; such an embedding extends uniquely to random variables (see [2]) and then the definition is equivalently rephrased as follows.…”

Section: A Isomorphismsmentioning

confidence: 99%

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On Standardness and I-cosiness

Laurent

2010

Séminaire De Probabilités XLIII

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Summary. The object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness without using Vershik's standardness criterion. The equivalence between I-cosiness and productness for homogeneous filtrations is further investigated by showing that the I-cosiness criterion is equivalent to Vershik's first level criterion separately for each random variable. We also aim to derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature.Acknowledgments. Financial support from the IAP research network (grant nr. P6/03 of the Belgian government, Belgian Science Policy) is gratefully acknowledged. I am also indebted to M. Émery for helpful and encouraging comments and suggestions on earlier drafts of this paper.

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Section: Example 350 (Stationary Markov Chain On a Denumerable Space)mentioning

confidence: 99%

Section: A Isomorphismsmentioning

confidence: 99%

On Standardness and I-cosiness

Laurent

2010

Séminaire De Probabilités XLIII

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“…Meyer (see [7,3]) and it is probably his last contribution to the general theory of stochastic processes. It was then used by Azéma and Yor [4] in the study of the set of zeros of continuous martingales and by Yor in an attempt to prove Barlow's conjecture on Brownian filtrations ( [19], and for a proof of Barlow's conjecture, see [5]). First, we give the definition of a saturated set, and then we cite a theorem of Azéma and Yor.…”

Section: Then There Exist Two Nonnegative and Continuous Local Martimentioning

confidence: 99%

Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales

Nikeghbali

2006

J Theor Probab

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Abstract. In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N + A, where the measure dA is carried by the set of zeros of Y . In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, these submartingales are the smallest ones. We also study some integrability questions in the multiplicative decomposition and interpret the notion of saturated sets in the light of our results.

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“…Then the one-point motion is a complex-valued martingale known as the spider martingale, see [5,Sect. 2].…”

Section: C Splitting: a Nonclassical Noisementioning

confidence: 99%

Nonclassical stochastic flows and continuous products

Tsirelson¹

2004

Probab. Surveys

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Autour d'un théorème de tsirelson sur des filtrations Browniennes et non Browniennes

Abstract: Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes

Cited by 61 publications

References 14 publications

On Standardness and I-cosiness

On Standardness and I-cosiness

Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales

Nonclassical stochastic flows and continuous products

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