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SOME LINEAR SPDEs DRIVEN BY A FRACTIONAL NOISE WITH HURST INDEX GREATER THAN 1/2.
- Source :
-
Infinite Dimensional Analysis, Quantum Probability & Related Topics . Dec2012, Vol. 15 Issue 4, p-1. 27p. - Publication Year :
- 2012
-
Abstract
- In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear stochastic partial differential equations (spde's) of parabolic and hyperbolic type. These equations rely on a spatial operator given by the L2-generator of a d-dimensional Lévy process X = (Xt)t≥0, and are driven by a spatially-homogeneous Gaussian noise, which is fractional in time with Hurst index H > 1/2. As an application, we consider the case when X is a β-stable process, with β ∈ (0, 2]. In the parabolic case, we develop a connection with the potential theory of the Markov process (defined as the symmetrization of X), and we show that the existence of the solution is related to the existence of a "weighted" intersection local time of two independent copies of . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02190257
- Volume :
- 15
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Infinite Dimensional Analysis, Quantum Probability & Related Topics
- Publication Type :
- Academic Journal
- Accession number :
- 86407658
- Full Text :
- https://doi.org/10.1142/S0219025712500233