Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 5

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: maximal function

Sortuj według:

Ogranicz wyniki do:

Weighted Maximal Inequalities for Martingale Transforms

Brzozowski Michał, Osękowski Adam

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 1

89--114

We study the weighted maximal L1-inequality for martingale transforms, under the assumption that the underlying weight satisfies Muckenhoupt’s condition A∞ and that the filtration is regular. The resulting linear dependence of the constant on the A∞ characteristic of the weight is optimal. The proof exploits certain special functions enjoying appropriate size conditions and concavity.

A Holistic State Equation for Timed Petri Nets

Werner M., Popova-Zeugmann L., Haustein M., Pelz E.

Fundamenta Informaticae

2014

Vol. 133, nr 2/3

305--322

In this paper we investigate Timed Petri nets (TPN) with fixed, possibly zero, durations and maximal step semantics. We define a new state representationwhere a state is a pair of a marking for the places and a marking for the transitions (a matrix of clocks). For this representation of states we provide an algebraic state equation. Such a state equation lets us prove a sufficient condition for the non-reachability of a state in a TPN. This application of the state equation is subsequently illustrated by an example.

Sharp inequalities for the square function of a nonnegative martingale

Osękowski A.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 1

61--72

We determine the optimal constants Cp and C*p p such that the following holds: if f is a nonnegative martingale and S(f) and f* denote its square and maximal functions, respectively, then ǁS(f)ǁp ≤Cp ǁfǁp; p < 1; and ǁS(f)ǁp ≤C*p ǁf*ǁp; p ≤1.

Maximal inequalities for stochastic integrals

Osękowski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 3

273-287

We find the optimal universal constant Cp (1 < p ≤ ∞) in the following inequality. If X = (Xt)t>o is a martingale and Y = [wzór] for some predictable process H taking values in [-1,1], then E[wzór].

Two inequalities for the first moments of a martingale, its square function and its maximal function

Osękowski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

441-449

Given a Hilbert space valued martingale (Mn), let (M∗n) and (Sn (M)) denote its maximal function and square function, respectively. We prove that E|Mn |≤ 2ESn (M), n = 0,1,2,…, EM∗n ≤ E|Mn| + 2ESn (M), n = 0,1,2,…. The first inequality is sharp, and it is strict in all nontrivial cases.