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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On a topological characterization of simple closed curve on the plane

100%
Weron A.
Commentationes Mathematicae
|
1973
|
tom 17
|
nr 1
EN
The article contains no abstract
2
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Banach-space-valued stationary processes and their linear prediction

69%
Chobanyan S. A., Weron A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
Contents 0. Introduction............................................................................................................................................. 5 1. Linear operators generated by random elements.......................................................................... 6 2. Covariance operator of generalized random elements................................................................. 9 3. The space of generalized random elements of the second-order as an LVH-space.............. 12 4. Banach-space-valued stationary processes................................................................................... 15 5. Correlation function and operator-valued measures..................................................................... 18 6. Ergodic properties................................................................................................................................. 23 7. Linear prediction problem.................................................................................................................... 26 8. J-regularity and J-singularity................................................................................................................ 29 9. $J_C$, $J_ψ$ and $J_∞$-singularity............................................................................................... 33 10. $J_∞$-regularity and factorization of operator-valued functions............................................... 36 References.................................................................................................................................................. 44
3
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On measure-preserving transformations and doubly stationary symmetric stable processes

64%
Gross A., Weron A.
Studia Mathematica
|
1995
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tom 114
|
nr 3
275-287
EN
In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms and the existence of σ-finite invariant measures. One consequence of the characterization is that all harmonizable symmetric stable processes are doubly stationary. Another consequence is that there exist stationary symmetric stable processes which are not doubly stationary.
4
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Pricing forward-start options in the HJM framework; evidence from the Polish market

64%
Sztuba P., Weron A.
Applicationes Mathematicae
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2001
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tom 28
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nr 2
211-224
EN
We show how to use the Gaussian HJM model to price modified forward-start options. Using data from the Polish market we calibrate the model and price this exotic option on the term structure. The specific problems of Central Eastern European emerging markets do not permit the use of the popular lognormal models of forward LIBOR or swap rates. We show how to overcome this difficulty.
5
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Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series

64%
Magdziarz M., Weron A.
Studia Mathematica
|
2007
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tom 181
|
nr 1
47-60
EN
We introduce a fractional Langevin equation with α-stable noise and show that its solution ${Y_{κ}(t), t ≥ 0}$ is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of $Y_{κ}(t)$ via the measure of its codependence r(θ₁,θ₂,t). We prove that $Y_{κ}(t)$ is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin equation.
6
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Chaotic behavior of infinitely divisible processes

51%
Cambanis S., Podgórski K., Weron A.
Studia Mathematica
|
1995
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tom 115
|
nr 2
109-127
EN
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
7
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Bounded solutions for ARMA model with varying coefficients

51%
Makagon A., Weron A., Wyłomańska A.
Applicationes Mathematicae
|
2004
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tom 31
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nr 3
273-285
EN
The paper deals with ARMA systems of equations with varying coefficients. A complete description of bounded solutions to ARMA(1,q) systems is obtained and their uniqueness is studied. Some special cases are discussed, including the case of significant interest of systems with periodic coefficients. The paper generalizes results of [9] and opens a new direction of study.
8
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On characterizations of interpolable and minimal stationary processes

38%
Weron A.
Studia Mathematica
|
1973-1974
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tom 49
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nr 2
165-183
9
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Dilations of Banach space operator valued functions

32%
Mlak W., Weron A.
Annales Polonici Mathematici
|
1980
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tom 38
|
nr 3
295-303
10
Content available remote

Aronszajn-Kolmogorov type theorems for positive definite kernels in locally convex spaces

32%
Górniak J., Weron A.
Studia Mathematica
|
1981
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tom 69
|
nr 3
235-246
11
Content available remote

q-variate minimal stationary processes

26%
Makagon A., Weron A.
Studia Mathematica
|
1976-1977
|
tom 59
|
nr 1
41-52
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