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)
Stability of analytical and numerical solutions for nonlinear stochastic delay differential equations with jumps. (English) Zbl 1236.60055
Summary: This paper is concerned with the stability of analytical and numerical solutions for nonlinear stochastic delay differential equations with jumps. A sufficient condition for the mean-square exponential stability of the exact solution is derived. Then, the mean-square stability of the numerical solution is investigated. It is shown that the compensated stochastic θ methods inherit the stability property of the exact solution. More precisely, the methods are mean-square stable for any stepsize Δt=τ/m when 1/2θ1, and they are exponentially mean-square stable if the stepsize Δt(0,Δt 0 ) when 0θ<1. Finally, some numerical experiments are given to illustrate the theoretical results.
MSC:
60H10Stochastic ordinary differential equations
65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations