DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS I: CONSTRUCTION AND QFT EXAMPLES

2001 ◽  
pp. 342-363 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis

DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS I: CONSTRUCTION AND QFT EXAMPLES

1989 ◽  
Vol 01 (02n03) ◽  
pp. 291-312 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
White Noise ◽  
Random Fields ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
Quantum Field ◽  
Quantum Fields ◽  
White Noise Analysis ◽  
Nikodym Derivative

Random fields are given in terms of measures which (in general) are singular with respect to that of white noise. However, many such measures can be expressed in terms of white noise through a positive generalized functional acting as a generalized Radon-Nikodym derivative. We give criteria for this to be the case and show that these criteria are fulfilled by Schwinger and Wightman functionals of various nontrivial quantum field theory models. Furthermore a number of closability criteria are given and discussed for the Dirichlet forms associated with positive generalized functionals of white noise. In a second paper we apply these results to the construction of Markov and of quantum fields.

scholarly journals Dirichlet Forms and White Noise Analysis

2001 ◽  
pp. 331-341
Author(s):  
T. Hida ◽  
J. Potthoff ◽  
L. Streit
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis

DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS II: CLOSABILITY AND DIFFUSION PROCESSES

1989 ◽  
Vol 01 (02n03) ◽  
pp. 313-323 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
White Noise ◽  
Diffusion Processes ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Dimensional Diffusion ◽  
White Noise Functionals ◽  
And Diffusion

It is shown that infinite dimensional Dirichlet forms as previously constructed in terms of (generalized) white noise functionals fit into the general framework of classical Dirichlet forms on topological vector spaces. This entails that all results obtained there are applicable. Admissible functionals give rise to infinite dimensional diffusion processes.

scholarly journals Dirichlet forms and white noise analysis

1988 ◽  
Vol 116 (2) ◽  
pp. 235-245 ◽  
Author(s):  
T. Hida ◽  
J. Potthoff ◽  
L. Streit
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis

White-noise analysis in retinal physiology

1986 ◽  
Vol 4 ◽  
pp. S141-S152
Author(s):  
Masanori Sakuranaga ◽  
Yu-Ichiro Ando ◽  
Ken-Ichi Naka
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
White Noise Analysis

A Poisson Structure in White-Noise Analysis

2009 ◽  
Author(s):  
R. Léandre ◽  
Piotr Kielanowski ◽  
S. Twareque Ali ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
...  
Keyword(s):  
White Noise ◽  
Poisson Structure ◽  
Noise Analysis ◽  
White Noise Analysis

WHITE NOISE ANALYSIS: SOME APPLICATIONS IN COMPLEX SYSTEMS, BIOPHYSICS AND QUANTUM MECHANICS

2012 ◽  
Vol 26 (29) ◽  
pp. 1230014 ◽  
Author(s):  
CHRISTOPHER C. BERNIDO ◽  
M. VICTORIA CARPIO-BERNIDO
Keyword(s):  
Quantum Mechanics ◽  
Probability Density Function ◽  
Complex Systems ◽  
White Noise ◽  
Noise Analysis ◽  
Social Systems ◽  
White Noise Analysis ◽  
The Past ◽  
White Noise Calculus ◽  
With Memory

The white noise calculus originated by T. Hida is presented as a powerful tool in investigating physical and social systems. Combined with Feynman's sum-over-all histories approach, we parameterize paths with memory of the past, and evaluate the corresponding probability density function. We discuss applications of this approach to problems in complex systems and biophysics. Examples in quantum mechanics with boundaries are also given where Markovian paths are considered.

scholarly journals ROLES OF LOG-CONCAVITY, LOG-CONVEXITY, AND GROWTH ORDER IN WHITE NOISE ANALYSIS

2001 ◽  
Vol 04 (01) ◽  
pp. 59-84 ◽  
Author(s):  
NOBUHIRO ASAI ◽  
IZUMI KUBO ◽  
HUI-HSIUNG KUO
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Holomorphic Functions ◽  
Legendre Transform ◽  
Legendre Functions ◽  
Growth Order ◽  
White Noise Analysis ◽  
Systematic Method ◽  
Growth Functions ◽  
Natural Way

In this paper we will develop a systematic method to answer the questions (Q1) (Q2) (Q3) (Q4) (stated in Sec. 1) with complete generality. As a result, we can solve the difficulties (D1) (D2) (discussed in Sec. 1) without uncertainty. For these purposes we will introduce certain classes of growth functions u and apply the Legendre transform to obtain a sequence which leads to the weight sequence {α(n)} first studied by Cochran et al.6 The notion of (nearly) equivalent functions, (nearly) equivalent sequences and dual Legendre functions will be defined in a very natural way. An application to the growth order of holomorphic functions on ℰc will also be discussed.

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