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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 18
  3. Journal of Fourier Analysis and Applications : Volume 18, Issue 6, December 2012
  4. Linear SPDEs Driven by Stationary Random Distributions
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 18, Issue 6, December 2012
Linear SPDEs Driven by Stationary Random Distributions
The Spherical Harmonic Spectrum of a Function with Algebraic Singularities
Full Spark Frames
Almost Sure Convergence of the Kaczmarz Algorithm with Random Measurements
Wavelet Analysis on Adeles and Pseudo-Differential Operators
Bilinear Fourier Restriction Theorems
Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators
On the One Sided Translates of Powers of Continuous Functions on Locally Compact Groups
Weighted Bounds for Variational Walsh–Fourier Series
Journal of Fourier Analysis and Applications : Volume 18, Issue 5, October 2012
Journal of Fourier Analysis and Applications : Volume 18, Issue 4, August 2012
Journal of Fourier Analysis and Applications : Volume 18, Issue 3, June 2012
Journal of Fourier Analysis and Applications : Volume 18, Issue 2, April 2012
Journal of Fourier Analysis and Applications : Volume 18, Issue 1, February 2012
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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Linear SPDEs Driven by Stationary Random Distributions

Content Provider SpringerLink
Author Balan, Raluca M.
Copyright Year 2012
Abstract Using tools from the theory of stationary random distributions developed in Itô (Mem. Coll. Sci., Univ. Kyoto, Ser. A: Math., 28:209–223, 1954) and Yaglom (Theory Probab. Appl., 2:273–320, 1957), we introduce a new class of processes which can be used as a model for the noise perturbing an SPDE. This type of noise is not necessarily Gaussian, but it includes the spatially homogeneous Gaussian noise introduced in Dalang (Electron. J. Probab. 4(6) 1999), and the fractional noise considered in Balan and Tudor (Stoch. Process. Appl., 120:2468–2494, 2010). We derive some general conditions for the existence of a random field solution of a linear SPDE with this type of noise, under some mild conditions imposed on the Green function of the differential operator which appears in this equation. This methodology is applied to the study of the heat and wave equations (possibly replacing the Laplacian by one of its fractional powers), extending in this manner the results of Balan and Tudor (Stoch. Process. Appl., 120:2468–2494, 2010) to the case H<1/2.
Ending Page 1145
Page Count 33
Starting Page 1113
File Format PDF
ISSN 10695869
e-ISSN 15315851
Journal Journal of Fourier Analysis and Applications
Issue Number 6
Volume Number 18
Language English
Publisher SP Birkhäuser Verlag Boston
Publisher Date 2012-08-03
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Stochastic partial differential equations Random fields Signal, Image and Speech Processing Processes with stationary increments Stochastic integral Stochastic integrals Abstract Harmonic Analysis Mathematical Methods in Physics Fourier Analysis Approximations and Expansions Fractional Brownian motion Partial Differential Equations Stationary random distributions
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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