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)
Strong stationary times via a new form of duality. (English) Zbl 0723.60083
The very interesting notion of SST (strong stationary time) of {\it D. Aldous} and {\it P. Diaconis} [Adv. Appl. Math. 8, 69-97 (1987; Zbl 0631.60065)] is extended to that of strong stationary duality for finite Markov chains (MC) $X\sb n$. Then the problem of analyzing convergence to stationarity is turned into a study of first passage times; it yields sharp bounds of the variation distance between the measure of $X\sb n$ and the stationary measure $\pi$. A general and often practical method for ergodic MC to construct SST is obtained. The chains with monotone likelihood ratio (especially death-and-birth chains), of which duals are particularly simply constructed, are discussed in detail with concrete examples. The relation of duals here to the notions of duality used by Liggett and Siegmund are considered.
Reviewer: M.Qian (Beijing)

60J10Markov chains (discrete-time Markov processes on discrete state spaces)
60G40Stopping times; optimal stopping problems; gambling theory
Full Text: DOI