scholarly journals Harmonic analysis of local times and sample functions of Gaussian processes

1969 ◽  
Vol 143 ◽  
pp. 269-269 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Harmonic Analysis ◽  
Gaussian Processes ◽  
Local Times

Predictive sets

2020 ◽  
pp. 2140006
Author(s):  
Nishant Chandgotia ◽  
Benjamin Weiss
Keyword(s):  
Harmonic Analysis ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Zero Entropy

A set [Formula: see text] is called predictive if for any zero entropy finite-valued stationary process [Formula: see text], [Formula: see text] is measurable with respect to [Formula: see text]. We know that [Formula: see text] is a predictive set. In this paper, we give sufficient conditions and necessary ones for a set to be predictive. We also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis.

Self-intersection local times for Gaussian processes in the plane

2014 ◽  
Vol 89 (1) ◽  
pp. 54-56
Author(s):  
A. A. Dorogovtsev ◽  
O. L. Izyumtseva
Keyword(s):  
Gaussian Processes ◽  
Local Times ◽  
Intersection Local Times

Local times of N-parameter Gaussian processes

2005 ◽  
Vol 15 (2) ◽  
pp. 108-114
Author(s):  
Lin Zhengyan ◽  
Cheng Zongmao
Keyword(s):  
Gaussian Processes ◽  
Local Times

scholarly journals On tail probability of local times of Gaussian processes

1999 ◽  
Vol 82 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Y. Kasahara ◽  
N. Kôno ◽  
T. Ogawa
Keyword(s):  
Gaussian Processes ◽  
Tail Probability ◽  
Local Times

scholarly journals Spatial Moduli of Non-Differentiability for Time-Fractional SPIDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 380
Author(s):  
Wensheng Wang
Keyword(s):  
Differential Equations ◽  
Heat Equation ◽  
White Noise ◽  
Harmonic Analysis ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Space Time ◽  
The Other ◽  
Moduli Of Continuity ◽  
Fractional Pdes

High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study spatial moduli of non-differentiability for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by space-time white noise. We use the underlying explicit kernels and spectral/harmonic analysis, yielding spatial moduli of non-differentiability for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. On the other hand, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of time fractional SPIDEs and their gradient.

scholarly journals Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wensheng Wang ◽  
Xiaoying Chang ◽  
Wang Liao
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Harmonic Analysis ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Colored Noise ◽  
Asymptotic Distributions ◽  
Heat Equations ◽  
Stochastic Heat Equations

Let u α , d = u α , d t , x ,   t ∈ 0 , T , x ∈ ℝ d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process u α , d , in time, having infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.

Results on Local Times of a Class of Multiparameter Gaussian Processes

2006 ◽  
Vol 22 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Zong-mao Cheng ◽  
Xiu-yun Wang ◽  
Zheng-yan Lin
Keyword(s):  
Gaussian Processes ◽  
Local Times
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