MULTIPLE INTEGRALS AND THE ISOMORPHISM BETWEEN A GENERAL WHITE NOISE SPACE AND A SYMMETRIC FOCK SPACE

1998 ◽  
pp. 245-259
Author(s):  
VOLKMAR LIEBSCHER
Keyword(s):  
White Noise ◽  
Fock Space ◽  
Multiple Integrals ◽  
White Noise Space

γ-product of white noise space and applications

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Samah Horrigue
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Fock Space ◽  
Wick Product ◽  
Uniqueness Of Solutions ◽  
White Noise Space

AbstractIn this paper, we define and give some characteristic properties of γ-product in white noise space, which is the generalization of the Wick product. Existence and uniqueness of solutions are proved for a certain class of ordinary differential equations for the Fock space.

scholarly journals A generalization of the Itô formula

2002 ◽  
Vol 31 (8) ◽  
pp. 477-496
Author(s):  
Said Ngobi
Keyword(s):  
Sobolev Space ◽  
White Noise ◽  
Itô Formula ◽  
Ito Formula ◽  
Integrable Functions ◽  
Square Integrable Functions ◽  
White Noise Space

The classical Itô formula is generalized to some anticipating processes. The processes we consider are in a Sobolev space which is a subset of the space of square integrable functions over a white noise space. The proof of the result uses white noise techniques.

scholarly journals White noise delta functions and continuous version theorem

1993 ◽  
Vol 129 ◽  
pp. 1-22
Author(s):  
Nobuaki Obata
Keyword(s):  
White Noise ◽  
Harmonic Analysis ◽  
Quantum Physics ◽  
Fock Space ◽  
Continuous Version ◽  
Infinite Dimensional ◽  
Schwartz Distribution ◽  
Delta Functions ◽  
Gelfand Triple ◽  
Gaussian Space

The recently developed Hida calculus of white noise [5] is an infinite dimensional analogue of Schwartz’ distribution theory besed on the Gelfand triple (E) ⊂ (L2) = L2 (E*, μ) ⊂ (E)*, where (E*, μ) is Gaussian space and (L2) is (a realization of) Fock space. It has been so far discussed aiming at an application to quantum physics, for instance [1], [3], and infinite dimensional harmonic analysis [7], [8], [13], [14], [15].

scholarly journals Linear Stochastic State Space Theory in the White Noise Space Setting

2010 ◽  
Vol 48 (8) ◽  
pp. 5009-5027 ◽  
Author(s):  
Daniel Alpay ◽  
David Levanony ◽  
Ariel Pinhas
Keyword(s):  
White Noise ◽  
State Space ◽  
Space Theory ◽  
Space Setting ◽  
State Space Theory ◽  
White Noise Space

COMPLEX WHITE NOISE ANALYSIS

2001 ◽  
Vol 04 (03) ◽  
pp. 347-375
Author(s):  
MYLAN REDFERN
Keyword(s):  
Stochastic Processes ◽  
White Noise ◽  
Fock Space ◽  
Noise Analysis ◽  
White Noise Analysis ◽  
Space Decomposition ◽  
New Space ◽  
Class Of Functions

This paper describes a new space, [Formula: see text], of complex Wiener distributions for the analysis of multi-parameter generalized stochastic processes [Formula: see text]. For a certain class of functions [Formula: see text] and complex Wiener integrals Φ1, …, Φm, F(Φ1, …, Φm) is defined as an element of [Formula: see text] and its Fock space decomposition determined.

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