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CRITERIA FOR THE CONTINUITY AND DIFFERENTIABILITY OF VECTOR PARAMETER PROCESSES
- Source :
- DTIC AND NTIS
- Publication Year :
- 1967
-
Abstract
- Let f(x) be a real or vector valued random process whose parameter set R is a bounded set in Euclidean n-space. Following the usual terminology, a version of f(x) is any process f tilde (x) defined on R which satisfies P(f(x) = f tilde (x)) =1 for each x epsilon R. It is sometimes useful to assert that there exists a version of f(x) which is (with probability one) continuous, Holder continuous, or perhaps differentiable in some component. Also estimates of the type P(sup (x epsilon R)/f(x)/> epsilon) may be desired for these versions. Illustrative examples are given.<br />Sponsored in part by National Aeronautics and Space Administration, Washington, D. C. Grant 40-002-015.
Details
- Database :
- OAIster
- Journal :
- DTIC AND NTIS
- Notes :
- text/html, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.ocn831490053
- Document Type :
- Electronic Resource