zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Mixing properties of Harris chains and autoregressive processes. (English) Zbl 0623.60087
The authors consider criteria for Markov processes (with stationary transitions, in discrete time, general state space) to be strongly mixing (α-mixing in usual terminology) or uniformly mixing (i.e., ϕ- mixing). They prove the very convenient result that a Harris-recurrent process which admits a nontrivial invariant measure is necessarily strongly mixing for any initial distribution. An example shows that the requirement of existence of an invariant measure cannot be dropped. It is also shown for the first-order autoregressive process Y n+1 =ρY n +e n+1 , where |ρ|<1 and {e n } is i.i.d. independent of Y 0 such that E log + |e 1 |< and j=1 n 0 ρ j e j has an absolutely continuous component, that if Y 0 is essentially bounded then {Y n } is uniformly mixing if and only if e 1 is essentially bounded.
Reviewer: E.Slud
MSC:
60J05Discrete-time Markov processes on general state spaces
60G10Stationary processes