Generalized level crossings and tangencies of a random field with smooth sample functions

Beth Allen

Stochastic Processes and their Applications, 1984, vol. 16, issue 3, 275-285

Abstract: 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.

Keywords: random; fields; regular; value; level; crossings; Sard's; Theorem; transversality; modulus; of; continuity; continuously; differentiable; sample; functions (search for similar items in EconPapers)
Date: 1984
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(84)90025-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:16:y:1984:i:3:p:275-285

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().