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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Własności graniczne procesów Markowa

100%
Urbanik K.
Instytut Matematyczny Polskiej Akademii Nauk
PL
SPIS RZEСZY Własności graniczne procesów Markowa................................................... 3 Bibliografia.................................................................................................. 41 Предельные свойства Марковских процессов(Резюме)........................ 42 Limit properties of Markoff processes (Summary)...................................... 44
2
Content available remote

A characterization of probability measures by f-moments

92%
Urbanik K.
Studia Mathematica
|
1996
|
tom 118
|
nr 2
185-204
EN
Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{∞} ƒ(x)μ^{*n}(dx)$ (n = 1,2...). A function ƒ is said to have the identification property} if probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function} if it is infinitely differentiable on the open half-line (0,∞) and $(-1)^{n} ƒ^{(n+1)}(x)$ is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.
3
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Moments of some random functionals

92%
Urbanik K.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 1
101-108
EN
The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals $\int_0^∞ f(X(τ,ω))dτ$ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.
4
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Functionals on transient stochastic processes with independent increments

92%
Urbanik K.
Studia Mathematica
|
1992
|
tom 103
|
nr 3
299-315
EN
The paper is devoted to the study of integral functionals $ʃ_0^∞ f(X(t,ω))dt$ for a wide class of functions f and transient stochastic processes X(t,ω) with stationary and independent increments. In particular, for nonnegative processes a random analogue of the Tauberian theorem is obtained.
5
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A duality principle for stationary random sequences

92%
Urbanik K.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 2
153-162
EN
The paper is devoted to the study of stationary random sequences. A concept of dual sequences is discussed. The main aim of the paper is to establish a relationship between the errors of linear least squares predictions for sequences and their duals.
6
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Uwagi o maksymalnej ilości bakterii w populacji

92%
Urbanik K.
Applicationes Mathematicae
|
1954
|
tom 2
|
nr 4
341-348
7
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Stability of stochastic processes defined by integral functionals

92%
Urbanik K.
Studia Mathematica
|
1992
|
tom 103
|
nr 3
225-238
EN
The paper is devoted to the study of integral functionals $ʃ_0^∞ f(X(t,ω)) dt$ for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals $ʃ_0^∞ f(aX(t,ω))dt$ with a ∈ (0,∞) is discussed.
8
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Musielak-Orlicz spaces and prediction problems

92%
Urbanik K.
Banach Center Publications
|
2004
|
tom 64
|
nr 1
207-219
EN
By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: $Xₙ(M) = ∫_{0}^{1} e^{2πnis}M(ds)$ (n = 0,±1,...) The paper deals with prediction problems for sequences {Xₙ(M)} for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for {Xₙ(M)} (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö's type for Musielak-Orlicz spaces in question. This leads to a characterization of deterministic sequences {Xₙ(M)} (n = 0,±1,...) in terms of random measures M.
9
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On a problem of S.L. Cheng concerning sequences of functions with convergent k-th differences

58%
Urbanik K.
Annales Polonici Mathematici
|
1959-1960
|
tom 7
|
nr 1
33-40
10
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The Conditional expectations and the ergodic theorem for strictly stationary generalized stochastic processes

58%
Urbanik K.
Studia Mathematica
|
1958
|
tom 17
|
nr 3
267-283
11
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Classes of measures closed under mixing and convolution. Weak stability

48%
Misiewicz J. K., Oleszkiewicz K., Urbanik K.
Studia Mathematica
|
2005
|
tom 167
|
nr 3
195-213
EN
For a random vector X with a fixed distribution μ we construct a class of distributions ℳ(μ) = {μ∘λ: λ ∈ 𝓟}, which is the class of all distributions of random vectors XΘ, where Θ is independent of X and has distribution λ. The problem is to characterize the distributions μ for which ℳ(μ) is closed under convolution. This is equivalent to the characterization of the random vectors X such that for all random variables Θ₁, Θ₂ independent of X, X' there exists a random variable Θ independent of X such that $XΘ₁ + X'Θ₂ \stackrel{d}{=} XΘ$. We show that for every X this property is equivalent to the following condition: ∀ a,b ∈ ℝ ∃ Θ independent of X, $aX + bX' \stackrel{d}{=} XΘ$. This condition reminds the characterizing condition for symmetric stable random vectors, except that Θ is here a random variable, instead of a constant. The above problem has a direct connection with the concept of generalized convolutions and with the characterization of the extreme points for the set of pseudo-isotropic distributions.
12
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Points-limites et points de continuité

48%
Knaster B., Mioduszewski J., Urbanik K.
Colloquium Mathematicum
|
1954-1955
|
tom 3
|
nr 2
164-169
13
Content available remote

A limit theorem for random variables in compact topological groups

47%
Ullrich M., Urbanik K.
Colloquium Mathematicum
|
1959-1960
|
tom 7
|
nr 2
191-198
14
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On the limiting probability distribution on a compact topological group

47%
Urbanik K.
Fundamenta Mathematicae
|
1957
|
tom 44
|
nr 3
253-261
15
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Remarks on congruence relations and weak automorphisms in abstract algebras

47%
Urbanik K.
Colloquium Mathematicum
|
1969
|
tom 20
|
nr 1
1-5
16
Content available remote

Bemerkungen über die mittlere Anzahl von Partikeln in gewissen stochastischen Schauern

47%
Urbanik K.
Studia Mathematica
|
1955-1956
|
tom 15
|
nr 1
34-42
17
Content available remote

Einige Bemerkungen über die Hirschman-Widder'schen Funktionen $H_{n,k}(x)$

43%
Łuszczki Z., Mikusiński J., Urbanik K., Wloka J., Zieleźny Z.
Colloquium Mathematicum
|
1956-1957
|
tom 4
|
nr 1
30-32
18
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Abstract algebras in which all elements are independent

41%
Marczewski E., Urbanik K.
Colloquium Mathematicum
|
1962
|
tom 9
|
nr 2
199-207
19
Content available remote

Analytical characterization of a composed, non-homogeneous Poisson process

41%
Fisz M., Urbanik K.
Studia Mathematica
|
1955-1956
|
tom 15
|
nr 3
328-336
20
Content available remote

Sur les espaces complets séparables de dimension 0

41%
Knaster B., Urbanik K.
Fundamenta Mathematicae
|
1953
|
tom 40
|
nr 1
194-202
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