Autor: Alpay, Daniel - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Finitely additive functions in measure theory and applications
Autorzy:: Alpay, Daniel
Jorgensen, Palle
Powiązania:: https://bibliotekanauki.pl/articles/29519748.pdf
Data publikacji:: 2024
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Hilbert space
reproducing kernel
probability space
Gaussian field
transforms
covariance
Itô integration
Itô calculus
generalized Brownian motion
Opis:: In this paper, we consider, and make precise, a certain extension of the Radon–Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators.
Źródło:: Opuscula Mathematica; 2024, 44, 3; 323-339
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Operators induced by certain hypercomplex systems
Autorzy:: Alpay, Daniel
Cho, Ilwoo
Powiązania:: https://bibliotekanauki.pl/articles/29519364.pdf
Data publikacji:: 2023
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: scaled hypercomplex ring
scaled hypercomplex monoids
representations
scaled-spectral forms
scaled-spectralization
Opis:: In this paper, we consider a family $ { \mathbb{H}_t }_{t∈\mathbb{R}} $ of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations $ {(\mathbb{C}^2, π_t)}_{t∈\mathbb{R} } $ of the hypercomplex system $ {\mathbb{H}_t }_{t∈\mathbb{R} } $, and study the realizations $ π_t (h) $ of hypercomplex numbers $ h ∈ \mathbb{H}_t $, as (2 × 2)-matrices acting on $ \mathbb{C}^2 $, for an arbitrarily fixed scale $ t ∈ \mathbb{R} $. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
Źródło:: Opuscula Mathematica; 2023, 43, 3; 275-333
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry
Autorzy:: Alpay, Daniel
Jorgensen, Palle E.T.
Powiązania:: https://bibliotekanauki.pl/articles/2051893.pdf
Data publikacji:: 2021
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: reproducing kernel
positive definite functions
approximation
algorithms
measures
stochastic processes
Opis:: We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.
Źródło:: Opuscula Mathematica; 2021, 41, 3; 283-300
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Stochastic Wiener filter in the white noise space
Autorzy:: Alpay, Daniel
Pinhas, Ariel
Powiązania:: https://bibliotekanauki.pl/articles/255216.pdf
Data publikacji:: 2020
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Wiener filter
white noise space
Wick product
stochastic distribution
Opis:: . In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white noise space theory to give an alternative characterization and a proper generalization to the Wiener filter over a suitable space of stochastic distributions introduced by Kondratiev. The main idea throughout this paper is to use the nuclearity of this space in order to view the random variables as bounded multiplication operators (with respect to the Wick product) between Hilbert spaces of stochastic distributions. This allows us to use operator theory tools and properties of Wiener algebras over Banach spaces to proceed and characterize the Wiener filter equations under the underlying randomness assumptions.
Źródło:: Opuscula Mathematica; 2020, 40, 3; 323-339
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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