Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Wick product

Sortuj według:

Ogranicz wyniki do:

Wick Calculus for Vector-valued Gaussian White Noise Functionals

Ji Un Cig, Ma Peng Cheng

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

283--302

Based on a Gel’fand triple (N) ⊗Ɛ ⊂Γ(H) ⊗h ⊂((N) ⊗Ɛ)∗, we introduce a new notion of Wick type product of generalized Gaussian white noise functionals which is associated with a continuous bilinear mapping B : Ɛ∗ ×Ɛ∗ → Ɛ∗. Then we study Wick type differential equations for vector-valued generalized Gaussian white noise functionals and, as a simple application, we study Wick type differential equations for matrix-valued generalized Gaussian white noise functionals. For our purposes, we make a systematic study of equicontinuity of the left and right Wick type multiplication operators.

Stochastic Wiener filter in the white noise space

Alpay Daniel, Pinhas Ariel

Opuscula Mathematica

2020

Vol. 40, no. 3

323--339

. 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.

An inequality for norms of Poisson Wick products

Lanconelli A., Stan A. I.

Probability and Mathematical Statistics

2013

Vol. 33, Fasc. 2

377--383

An inequality for the norms of Poisson Wick products, involving second quantization operators, will be presented.

White noise based stochastic calculus associated with a class of Gaussian processes

Alpay D., Attia H., Levanony D.

Opuscula Mathematica

2012

Vol. 32, no. 3

401-422

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.