Temat: white noise space - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: White noise based stochastic calculus associated with a class of Gaussian processes
Autorzy:: Alpay, D.
Attia, H.
Levanony, D.
Powiązania:: https://bibliotekanauki.pl/articles/254849.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: white noise space
Wick product
stochastic integral
Opis:: Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.
Źródło:: Opuscula Mathematica; 2012, 32, 3; 401-422
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
Autorzy:: Alpay, D.
Kipnis, A.
Powiązania:: https://bibliotekanauki.pl/articles/255154.pdf
Data publikacji:: 2013
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: stochastic integral
white noise space
fractional Brownian motion
Opis:: Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.
Źródło:: Opuscula Mathematica; 2013, 33, 3; 395-417
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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

Skocz do pozycji: 4.

Tytuł:: A sampling theory for infinite weighted graphs
Autorzy:: Jorgensen, P. E. T.
Powiązania:: https://bibliotekanauki.pl/articles/254989.pdf
Data publikacji:: 2011
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: weighted graph
Hilbert space
Laplace operator
sampling
Shannon
white noise
Wiener transform
interpolation
Opis:: We prove two sampling theorems for infinite (countable discrete) weighted graphs G; one example being "large grids of resistors" i.e., networks and systems of resistors. We show that there is natural ambient continuum X containing G, and there are Hilbert spaces of functions on X that allow interpolation by sampling values of the functions restricted only on the vertices in G. We sample functions on X from their discrete values picked in the vertex-subset G. We prove two theorems that allow for such realistic ambient spaces X for a fixed graph G, and for interpolation kernels in function Hilbert spaces on X, sampling only from points in the subset of vertices in G. A continuum is often not apparent at the outset from the given graph G. We will solve this problem with the use of ideas from stochastic integration.
Źródło:: Opuscula Mathematica; 2011, 31, 2; 209-236
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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