Successive approximation of neutral functional stochastic differential equations with jumps

Statistics and Probability Letters

Volumn 80, Issue 5-6, 2010, Pages 324-332

  Boufoussi, Brahim ^a   Hajji, Salah ^a  

^a FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 74849121966     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2009.11.006     Document Type: Article

References (18)

1. Albeverio S., Mandrekar V., and Rüdiger B. Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise. Stochastic Process. Appl. 119 (2009) 835-863
2. Bihari I. A generalization of a lemma of Belmman and its application to uniqueness problem of differential equations. Acta. Math., Acad. Sci. Hungar. 7 (1956) 71-94
3. Caraballo T., Real J., and Taniguchi T. The exponential stability of neutral stochastic delay partial differential equations. Discrete Contin. Dyn. Syst. 18 (2007) 295-313
4. Da Prato G., and Zabczyk J. Stochastic Equations in Infinite Dimensions (1992), Cambridge University Press, Cambridge
5. Datko R. Linear autonomous neutral differential equations in Banach spaces. J. Differential Equations 25 (1977) 258-274
6. Goldstein A., and Jerome. Semigroups of linear operators and applications. Oxford Mathematical Monographs (1985), The Clarendon Press, Oxford University Press, New York
7. Govindan T.E. Almost sure exponential stability for stochastic neutral partial functional differential equations. Stochastics 77 (2005) 139-154
8. Hausenblas E., and Seidler J. Stochastic convolutions driven by martingales: Maximal inequalities and exponential integrability. Stoch. Anal. Appl. 26 1 (2008) 98-119
9. Ikeda N., and Watanabe S. Stochastic Differential Equations and Diffusion Processes (1989), Nort-Holland, Kodansha, Amsterdam, Oxford, New York
10. Kolmanovskii V., Koroleva N., Maizenberg T., Mao X., and Matasov A. Neutral stochastic differential delay equations with Markovian switching. Stoch. Anal. Appl. 21 4 (2003) 819-847
11. Kolmanovskii V.B., and Nosov V.R. Stability of Functional Differential Equations (1986), Academic Press
12. Liu K. Uniform stability of autonomous linear stochastic fuctional diferential equations in infinite dimensions. Stochastic Process. Appl. 115 (2005) 1131-1165
13. Liu K., and Xia X. On the exponential stability in mean square of neutral stochastic functional differential equations. Systems Control Lett. 37 4 (1999) 207-215
14. Mahmudov N.I. Existence and uniqueness results for neutral SDEs in Hilbert spaces. Stochastic Analysis and Applications 24 (2006) 79-95
15. Mao X. Exponential stability in mean square of neutral stochastic differential functional equations. Systems Control Lett. 26 (1995) 245-251
16. Mao X. Razumikhin-type theorems on exponential stability of neutral stochastic functional-differential equations. SIAM J. Math. Anal. 28 2 (1997) 389-401
17. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences vol. 44 (1983), Springer-Verlag, New York
18. Wu J. Theory and Applications of Partial Functional Differential Equations. Applied Mathematical Sciences vol. 119 (1996), Springer-Verlag, New York