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• W1651035311 abstract "Using tools from the theory of random fields with stationary increments, we introduce a new class of processes which can be used as a model for the noise perturbing an SPDE. This type of noise (called harmonizable) is not necessarily Gaussian, but it includes the spatially homogeneous Gaussian noise introduced in Dalang (1999), and the fractional noise considered in Balan and Tudor (2010). We derive some general conditions for the existence of a random field solution of a linear SPDE with harmonizable 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 (2010) to the case $H<1/2$." @default.
• W1651035311 created "2016-06-24" @default.
• W1651035311 creator A5000263001 @default.
• W1651035311 date "2011-08-13" @default.
• W1651035311 modified "2023-09-27" @default.
• W1651035311 title "Linear SPDEs with harmonizable noise" @default.
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• W1651035311 hasPublicationYear "2011" @default.
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