Wszystkie pola: Itô integration - 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

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Skocz do pozycji: 2.

Tytuł:: Decomposition of Gaussian processes, and factorization of positive definite kernels
Autorzy:: Jorgensen, Palie E. T.
Tian, Feng
Powiązania:: https://bibliotekanauki.pl/articles/255819.pdf
Data publikacji:: 2019
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: reproducing kernel Hilbert space frames
generalized Ito-integration
the measurable category analysis/synthesis
interpolation
Gaussian free fields
non-uniform sampling
optimization
transform
covariance
feature space
Opis:: We establish a duality for two lactorization questions, one for general positive definite (p.d.) kernels K, and the other for Gaussian processes, say V. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel K, presented as a covariance kernel for a Gaussian process V. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel K, vs for Gaussian process V. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for K is the exact same as that which yield factorizations for V. Examples and applications are included: point-processes, sampling schemes, constructive discretization, graph-Laplacians, and boundary-value problems.
Źródło:: Opuscula Mathematica; 2019, 39, 4; 497-541
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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