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)
Quadratic stochastic operators and processes: results and open problems. (English) Zbl 1242.60067
This paper reviews the modern developments of the theory and applications of quadratic stochastic operators initiated by S. Bernstein in 1924, based in large part on the literature published by the authors in non-English journals over the past 20 years. This broad overview is motivated by the use of quadratic stochastic operators in discrete-time population genetics, and more generally it includes the connections of quadratic operators and processes in classical, and quantum, probability with biology, genetics, population dynamics, and physics. The paper covers discrete dynamical systems and continuous-time stochastic processes generated by quadratic stochastic operators, as well as quantum quadratic stochastic operators and associated processes.
MSC:
60H25Random operators and equations
60G07General theory of stochastic processes
37N25Dynamical systems in biology
46L53Noncommutative probability and statistics
60J28Applications of continuous-time Markov processes on discrete state spaces