Hermitian random measures and spectral representations
The aim of this chapter is to analyze more deeply the class of random variables encountered in Example 8.5.4. In particular, we shall consider complex-valued functions ϕ, to which we associate real-valued (multiple) stochastic integrals. This type of construction is used in the spectral theory of time series and, in particular, in the context of self-similar processes (see e.g., [12, 23, 34, 66, 151, 153]).
KeywordsSpectral Representation Fractional Brownian Motion Real Hilbert Space Spectral Domain Gaussian Measure
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