A recurrence theorem for square-integrable martingales

Gerold Alsmeyer

Displaying similar documents to “A recurrence theorem for square-integrable martingales”

Embedding of random vectors into continuous martingales

E. Dettweiler (1999)

Studia Mathematica

Similarity:

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 $\tilde{Ω}$ of Ω, and a filtration ${({\tilde{ℱ}}_{t})}_{t \geq 0}$ on $\tilde{Ω}$ , such that for every $X \in L^{0} (Ω, E)$ there is an E-valued, continuous $({\tilde{ℱ}}_{t})$ -martingale ${(M_{t} (X))}_{t \geq 0}$ 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 $X \in L^{0} (Ω, ℝ)$ , and for general E this leads to a representation of random...

On sums of i.i.d. random variables indexed by N parameters

Davar Khoshnevisan (2000)

Séminaire de probabilités de Strasbourg

Similarity:

Attainable claims with p'th moments

F. Delbaen, W. Schachermayer (1996)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

A note on $L_{2}$ maximal inequalities

Jim Pitman (1981)

Séminaire de probabilités de Strasbourg

Similarity:

Disjointification of martingale differences and conditionally independent random variables with some applications

Sergey Astashkin, Fedor Sukochev, Chin Pin Wong (2011)

Studia Mathematica

Similarity:

Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form ${f_{k} (s) x_{k} (t)}_{k = 1} ⁿ$ , where $f_{k}$ ’s are independent and xk’s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables...

Singular measures and the little bloch space.

Alicia Cantón (1998)

Publicacions Matemàtiques

Similarity:

Aleksandrov, Anderson and Nicolau have found examples of inner functions that are in the little Bloch space with a specific rate of convergence to zero. As a corollary they obtain positive singular measures defined in the boundary of the unit disc that are simultaneously symmetric and Kahane. Nevertheless their construction is very indirect. We give an explicit example of such measures by means of a martingale argument.

Differentiability of multiplicative processes related to branching random walks

Julien Barral (2000)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

On a generalization of a theorem of W. Sudderth and some applications

A. Engelbert, H. Engelbert (1980)

Banach Center Publications

Similarity:

A note on dilations and martingales.

Jones, Martin L. (1993)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Carthaginian enlargement of filtrations

Giorgia Callegaro, Monique Jeanblanc, Behnaz Zargari (2013)

ESAIM: Probability and Statistics

Similarity:

This work is concerned with the theory of initial and progressive enlargements of a reference filtration $𝔽$ F with a random time. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an $𝔽$ F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as...