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)
On the pth moment exponential stability criteria of neutral stochastic functional differential equations. (English) Zbl 1115.60065
The classical version of the Lyapunov direct method is difficult to be applied for stochastic differential equations containing delay in the state variable. Criteria are presented which are relatively easy to verify when the pth moment exponential stability of the solutions is used. The results of Liu and Xia regarding the exponential stability in mean square are generalized to the pth moment stability, p2. The paper contains a lemma proving some estimates of the solutions when the pth norm is used. The main results are presented in two theorems extending the estimates already obtained and proving sufficient conditions for pth moment exponential stability. All proofs are explicitly given and a patient reader will understand the subject. Some numerical examples are added.
MSC:
60H20Stochastic integral equations