Introduction to Gaussian Processes

نویسنده

  • STEVEN P. LALLEY
چکیده

Definition 1.1. A Gaussian process {Xt }t∈T indexed by a set T is a family of (real-valued) random variables Xt , all defined on the same probability space, such that for any finite subset F ⊂ T the random vector XF := {Xt }t∈F has a (possibly degenerate) Gaussian distribution; if these finitedimensional distributions are all non-degenerate then the Gaussian process is said to be nondegenerate. Equivalently, {Xt }t∈T is Gaussian if every finite linear combination � t∈F a t Xt is either identically zero or has a Gaussian distribution on R. A Gaussian process {Xt }t∈T is centered if E Xt = 0 for every t ∈ T , and its covariance function is the (symmetric) bivariate function

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تاریخ انتشار 2013