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)
Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations. (English) Zbl 1232.60046
The authors derive new criteria for asymptotic stability and boundedness of solutions of stochastic functional differential equations, whereby the linear growth condition is replaced by a more general condition.
60H10Stochastic ordinary differential equations
93E15Stochastic stability
[1]Appleby, J. A. D.; Reynolds, D. W.: Decay rates of solutions of linear stochastic Volterra equations, Electron. J. Probab. 13, 922-943 (2008) · Zbl 1188.45008 · doi:emis:journals/EJP-ECP/_ejpecp/viewarticle5c1b.html
[2]Appleby, J. A. D.; Rodkina, A.: Stability of nonlinear stochastic Volterra difference equations with respect to a fading perturbation, Int. J. Difference equ. 4, 165-184 (2009)
[3]Bahar, A.; Mao, X.: Persistence of stochastic power law logistic model, J. appl. Probab. stat. 3, No. 1, 37-43 (2008)
[4]Basin, M.; Rodkina, A.: On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays, Nonlinear anal. 68, 2147-2157 (2008) · Zbl 1154.34044 · doi:10.1016/j.na.2007.01.046
[5]Khasminskii, R. Z.: Stochastic stability of differential equations, (1969)
[6]Kolmanovskii, V.; Myshkis, A.: Applied theory of functional differential equations, (1992)
[7]Kolmanovskii, V. B.; Nosov, V. R.: Stability and periodic modes of control systems with aftereffect, (1981) · Zbl 0457.93002
[8]Lipster, R. Sh.; Shiryayev, A. N.: Theory of martingales, (1989)
[9]Loève, M.: Probability theory, (1963)
[10]Mao, X.: Stability of stochastic differential equations with respect to semimartingales, (1991)
[11]Mao, X.: Exponential stability of stochastic differential equations, (1994)
[12]Mao, X.: Exponential stability in mean square of neutral stochastic differential functional equations, Syst. control lett. 26, 245-251 (1995) · Zbl 0877.93133 · doi:10.1016/0167-6911(95)00018-5
[13]Mao, X.: Razumikhin type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. anal. 28, No. 2, 389-401 (1997) · Zbl 0876.60047 · doi:10.1137/S0036141095290835
[14]Mao, X.: Stochastic differential equations and applications, (2007)
[15]Mao, X.; Yuan, C.: Stochastic differential equations with Markovian switching, (2006) · Zbl 1109.60043 · doi:10.1155/JAMSA/2006/59032
[16]Mohammed, S. -E.A.: Stochastic functional differential equations, (1986)
[17]Natanson, I. P.: Theory of functions of real variables, vol. 1, (1964)
[18]Rodkina, A.; Basin, M.: On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term, Syst. control lett. 56, 423-430 (2007) · Zbl 1124.93066 · doi:10.1016/j.sysconle.2006.11.001
[19]Shu, Z.; Lam, J.; Xu, S.: Improved exponential estimates for neutral systems, Asian J. Control 11, 261-270 (2009)
[20]Yang, R.; Gao, H.; Lam, J.; Shi, P.: New stability criteria for neural networks with distributed and probabilistic delays, Circuits syst. Signal process 28, 505-522 (2009) · Zbl 1170.93027 · doi:10.1007/s00034-008-9092-1
[21]Yuan, C.; Lygeros, J.: Stabilization of a class of stochastic differential equations with Markovian switching, Syst. control lett. 54, 819-833 (2005) · Zbl 1129.93517 · doi:10.1016/j.sysconle.2005.01.001
[22]Yuan, C.; Lygeros, J.: Asymptotic stability and boundedness of delay switching diffusions, IEEE trans. Automat. control 51, 171-175 (2006)