Asymptotic expansions for functions of the increments of certain Gaussian processes
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])<[infinity], where [eta]=N(0,1). When [sigma]2 is regularly varying at zero and is locally integrable for some integer j0>=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 .
Year of publication: |
2010
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Authors: | Marcus, Michael B. ; Rosen, Jay |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 120.2010, 2, p. 195-222
|
Publisher: |
Elsevier |
Subject: | Gaussian processes Asymptotic expansions |
Saved in:
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