Distribution Function Inequalities for Martingales
نویسندگان
چکیده
منابع مشابه
Concentration Inequalities for Semi-bounded Martingales
In this paper we extend the results of de la Peña [3]. The main method that we use is the theory of decoupling, which has been developed in de la Peña [2] and [3]. Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. We will apply the theory of decoupling as in de la Peña [3] and some new inequalities for indepen...
متن کاملDistribution function inequalities for singular integrals.
This paper describes some distribution function inequalities between maximal functions and singular integral operators.
متن کاملRandom Martingales and Localization of Maximal Inequalities
Let (X, d, μ) be a metric measure space. For ∅ 6= R ⊆ (0,∞) consider the Hardy-Littlewood maximal operator MRf(x) def = sup r∈R 1 μ(B(x, r)) ∫
متن کاملOn Probability and Moment Inequalities for Supermartingales and Martingales∗
(Translated by the author) Abstract. The probability inequality for maxk≤n Sk, where Sk = ∑k j=1 Xj , is proved under the assumption that the sequence Sk, k = 1, . . . , n is a supermartingale. This inequality is stated in terms of probabilities P(Xj > y) and conditional variances of random variables Xj , j = 1, . . . , n. As a simple consequence the well-known moment inequality due to Burkhold...
متن کاملOn the Maximal Inequalities for Martingales Involving Two Functions
Let Φ(t) and Ψ(t) be nonnegative convex functions, and let φ and ψ be the right continuous derivatives of Φ and Ψ, respectively. In this paper, we prove the equivalence of the following three conditions: (i) ‖f∗‖Φ ≤ c‖f‖Ψ, (ii) LΨ ⊆ HΦ and (iii) ∫ t s0 φ(s) s ds ≤ cψ(ct), ∀t > s0, where LΨ and HΦ are the Orlicz martingale spaces. As a corollary, we get a sufficient and necessary condition under...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1973
ISSN: 0091-1798
DOI: 10.1214/aop/1176997023