scholarly journals Solutions of Hyperbolic Stochastic PDEs on Bounded and Unbounded Domains

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Sandro Coriasco ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Stochastic Partial Differential Equations ◽  
Input Data ◽  
Fourier Integral Operator ◽  
Noise Analysis ◽  
Unbounded Domains ◽  
Fourier Integral ◽  
Stochastic Pdes ◽  
White Noise Analysis ◽  
Kondratiev Spaces ◽  
Temporal And Spatial

AbstractWe treat several classes of hyperbolic stochastic partial differential equations in the framework of white noise analysis, combined with Wiener–Itô chaos expansions and Fourier integral operator methods. The input data, boundary conditions and coefficients of the operators are assumed to be generalized stochastic processes that have both temporal and spatial dependence. We prove that the equations under consideration have unique solutions in the appropriate Sobolev–Kondratiev or weighted-Sobolev–Kondratiev spaces. Moreover, an explicit chaos form of the solutions is obtained, useful for calculating expectations, variances and higher order moments of the solution.

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.

scholarly journals Assessment of the validity of parameters describing temporal and spatial characteristics of spontaneous infant activity in the period of fidgety movements

2020 ◽  
Author(s):  
Iwona Doroniewicz ◽  
Daniel Ledwoń ◽  
Monika Bugdol ◽  
Katarzyna Kieszczyńska ◽  
Alicja Affanasowicz ◽  
...  
Keyword(s):  
Input Data ◽  
Head Position ◽  
Lower Limbs ◽  
Movement Behavior ◽  
Psychomotor Development ◽  
Spatial Characteristics ◽  
Spontaneous Movements ◽  
Depth Analysis ◽  
Temporal And Spatial ◽  
Temporal And Spatial Characteristics

Abstract Background: The assessment of spontaneous activity of infants is of fundamental importance to the diagnosis and prediction of abnormal psychomotor development in children. Comprehensive and early diagnosis allows for quick and effective treatment and therapy. Subjective methods are based on the knowledge and experience of the diagnostician. The lack of objective methods to assess the motor development of infants makes it necessary to search for solutions for reliable, credible, and reproducible assessment expressed in numerical or pictorial terms. This study discusses the possibilities of pictorial standardization and optimization of measurable infant behavior based on video recordings. Methods: The authors attempt to perform computer analysis of spontaneous movements depending on the left, right, and front head position. The study was based on data of 26 healthy infants aged 7 to 15 weeks, with three infants included in an in-depth analysis. The selected films represented the input data for the parameters used as the author's temporal and spatial characteristics describing the global movements of the upper and lower limbs. The obtained videos were used as the input data for the algorithm of automatic detection of characteristic points using the OpenPose library. Results: The following movement characteristics were analysed: Factor of Movement's Area (FMA) ("amount of movement in the movement"), Factor of Movement's Shape (FMS) ("circularity” or "ellipticity" of the movement), Center of Movement's Area (CMA) ("inward and outward" and "up and down" movements). Preliminary analysis of the videos showed that the activity of the limbs, especially the upper limbs, may depend on the position of the head.Conclusions: The movement behavior of the infants varies in terms of the range and quality of movement, depending on age and head position.

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