zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Grey noise. (English) Zbl 0761.60036
Ideas and methods in mathematical analysis, stochastics and applications. In memory of R. Høegh-Krohn, Vol. 1, 261-282 (1992).
Summary: The Mittag-Leffler function $E\sb \alpha$ is completely monotonic on ${\bold R}\sb -$ for $0<\alpha\le 1$. This remarkable fact is exploited to define a probability measure $\tau\sb \alpha$ on a Hilbert triple $K\sb \alpha\subset H\sb \alpha\subset K\sb \alpha'$. This measure is called grey noise. It reduces to white noise for $\alpha=1$. Mimicking the construction of Brownian motion yields its grey variant. The sample paths of grey Brownian motion are Hölder continuous with index arbitrarily close to $\alpha/2$. The well-known relation between Brownian motion and diffusion carries over to grey Brownian motion and fractional diffusion with time derivative of order $\alpha$. For the entire collection see [Zbl 0764.00003].

60G20Generalized stochastic processes
60G17Sample path properties