Asymptotic expansions for functions of the increments of certain Gaussian processes

Michael B. Marcus and Jay Rosen

Stochastic Processes and their Applications, 2010, vol. 120, issue 2, 195-222

Abstract: Let G={G(x),x>=0} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a function with Ef2([eta]) =1, and satisfies some additional regularity conditions, in L2. Here Hj is the jth Hermite polynomial. Also :(G')j:(I[a,b]) is a jth order Wick power Gaussian chaos constructed from the Gaussian field G'(g), with covariance where .

Keywords: Gaussian; processes; Asymptotic; expansions (search for similar items in EconPapers)
Date: 2010
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