Generalized level crossings and tangencies of a random field with smooth sample functions
Tangencies and level crossings of a random field X:m+x[Omega]-->n (which is not necessarily Gaussian) are studied under the assumption that almost every sample path is continuously differentiable. If n=m and if the random field has uniformly bounded sample derivatives and uniformly bounded densities for the distributions of the Xl, then for a compact K[subset of]m+ and any fixed level, the restriction to K of almost every sample path has no tangencies to the level and at most finitely many crossings. The case of n[not equal to]m is also examined. Some generic properties, which hold for a residual set of random fields, are analyzed. Proofs involve the concepts of regularity and transversality from differential topology.
Year of publication: |
1984
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Authors: | Allen, Beth |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 16.1984, 3, p. 275-285
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Publisher: |
Elsevier |
Keywords: | random fields regular value level crossings Sard's Theorem transversality modulus of continuity continuously differentiable sample functions |
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