Abstract
Suppose {X(t), t ∈ Gd} is a random field in d dimensions, with d ∈ ℤ+; that is, {X(t), t ∈ Gd} is a collection of random variables X(t) taking values in a state space S, defined on a probability space (Ω, A, P), and indexed by the variable t ∈ Gd. Throughout this chapter, G will stand for either the set of real numbers ℝ, or the set of integers ℤ; thus, the random field {X(t)} is allowed to “run” in either continuous or discrete “time.” Similarly, G+ will denote ℝ+ or ℤ+ (the sets of positive real numbers and integers, respectively) according to whether G = ℝ or G = ℤ.
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© 1999 Springer Science+Business Media New York
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Politis, D.N., Romano, J.P., Wolf, M. (1999). Subsampling for Random Fields. In: Subsampling. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1554-7_5
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DOI: https://doi.org/10.1007/978-1-4612-1554-7_5
Publisher Name: Springer, New York, NY
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