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Khasminskiitype theorems for stochastic functional differential equations
1.  Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China 
2.  Department of Applied Mathematics, Donghua Univerisity, Shanghai 201600, China 
3.  Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH 
4.  School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China 
References:
[1] 
A. Bahar and X. Mao, Stochastic delay LotkaVolterra model, J. Math. Anal. Appl., 292 (2004), 364380. doi: 10.1016/j.jmaa.2003.12.004. Google Scholar 
[2] 
A. Bahar and X. Mao, Stochastic delay population dynamics, International J. Pure and Applied Math., 11 (2004), 377400. Google Scholar 
[3] 
T. C. Gard, "Introduction to Stochastic Differential Equations," Monographs and Textbooks in Pure and Applied Mathematics, 114, Marcel Dekker, Inc., New York, 1988. Google Scholar 
[4] 
R. Z. Has'minskiĭ, "Stochastic Stability of Differential Equations," Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, 7, Sijthoff & Noordhoff, Alphen aan den RijnGermantown, Md., 1980. Google Scholar 
[5] 
V. Kolmanovskiĭ and A. Myshkis, "Applied Theory of FunctionalDifferential Equations," Mathematics and its Applications (Soviet Series), 85, Kluwer Academic Publishers Group, Dordrecht, 1992. Google Scholar 
[6] 
G. S. Ladde and V. Lakshmikantham, "Random Differential Inequalities," Mathematics in Science and Engineering, 150, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New YorkLondon, 1980. Google Scholar 
[7] 
M. Loève, "Probability Theory," Third edition, D. Van Nostrand Company, Inc., Princeton, N. J.Toronto, Ont.London, 1963. Google Scholar 
[8] 
Q. Luo, X. Mao and Y. Shen, Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations, Automatica J. IFAC, 47 (2011), 20752081. doi: 10.1016/j.automatica.2011.06.014. Google Scholar 
[9] 
X. Mao, "Stability of Stochastic Differential Equations with Respect to Semimartingales," Pitman Research Notes in Mathematics Series, 251, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1991. Google Scholar 
[10] 
X. Mao, "Exponential Stability of Stochastic Differential Equations," Monographs and Textbooks in Pure and Applied Mathematics, 182, Marcel Dekker, Inc., New York, 1994. Google Scholar 
[11] 
X. Mao, "Stochastic Differential Equations and Applications," Second edition, Horwood Publishing Limited, Chichester, 2008. Google Scholar 
[12] 
X. Mao, A note on the LaSalletype theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268 (2002), 125142. doi: 10.1006/jmaa.2001.7803. Google Scholar 
[13] 
X. Mao and M. J. Rassias, Khasminskiitype theorems for stochastic differential delay equations, J. Sto. Anal. Appl., 23 (2005), 10451069. doi: 10.1080/07362990500118637. Google Scholar 
[14] 
X. Mao and C. Yuan, "Stochastic Differential Equations with Markovian Switching," Imperial College Press, London, 2006. Google Scholar 
[15] 
X. Mao, C. Yuan and J. Zou, Stochastic differential delay equations in population dynamics, J. Math. Anal. Appl., 304 (2005), 296320. doi: 10.1016/j.jmaa.2004.09.027. Google Scholar 
[16] 
S. E. A. Mohammed, "Stochastic Functional Differential Equations," Research Notes in Mathematics, 99, Pitman (Advanced Publishing Program), Boston, MA, 1984. Google Scholar 
show all references
References:
[1] 
A. Bahar and X. Mao, Stochastic delay LotkaVolterra model, J. Math. Anal. Appl., 292 (2004), 364380. doi: 10.1016/j.jmaa.2003.12.004. Google Scholar 
[2] 
A. Bahar and X. Mao, Stochastic delay population dynamics, International J. Pure and Applied Math., 11 (2004), 377400. Google Scholar 
[3] 
T. C. Gard, "Introduction to Stochastic Differential Equations," Monographs and Textbooks in Pure and Applied Mathematics, 114, Marcel Dekker, Inc., New York, 1988. Google Scholar 
[4] 
R. Z. Has'minskiĭ, "Stochastic Stability of Differential Equations," Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, 7, Sijthoff & Noordhoff, Alphen aan den RijnGermantown, Md., 1980. Google Scholar 
[5] 
V. Kolmanovskiĭ and A. Myshkis, "Applied Theory of FunctionalDifferential Equations," Mathematics and its Applications (Soviet Series), 85, Kluwer Academic Publishers Group, Dordrecht, 1992. Google Scholar 
[6] 
G. S. Ladde and V. Lakshmikantham, "Random Differential Inequalities," Mathematics in Science and Engineering, 150, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New YorkLondon, 1980. Google Scholar 
[7] 
M. Loève, "Probability Theory," Third edition, D. Van Nostrand Company, Inc., Princeton, N. J.Toronto, Ont.London, 1963. Google Scholar 
[8] 
Q. Luo, X. Mao and Y. Shen, Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations, Automatica J. IFAC, 47 (2011), 20752081. doi: 10.1016/j.automatica.2011.06.014. Google Scholar 
[9] 
X. Mao, "Stability of Stochastic Differential Equations with Respect to Semimartingales," Pitman Research Notes in Mathematics Series, 251, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1991. Google Scholar 
[10] 
X. Mao, "Exponential Stability of Stochastic Differential Equations," Monographs and Textbooks in Pure and Applied Mathematics, 182, Marcel Dekker, Inc., New York, 1994. Google Scholar 
[11] 
X. Mao, "Stochastic Differential Equations and Applications," Second edition, Horwood Publishing Limited, Chichester, 2008. Google Scholar 
[12] 
X. Mao, A note on the LaSalletype theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268 (2002), 125142. doi: 10.1006/jmaa.2001.7803. Google Scholar 
[13] 
X. Mao and M. J. Rassias, Khasminskiitype theorems for stochastic differential delay equations, J. Sto. Anal. Appl., 23 (2005), 10451069. doi: 10.1080/07362990500118637. Google Scholar 
[14] 
X. Mao and C. Yuan, "Stochastic Differential Equations with Markovian Switching," Imperial College Press, London, 2006. Google Scholar 
[15] 
X. Mao, C. Yuan and J. Zou, Stochastic differential delay equations in population dynamics, J. Math. Anal. Appl., 304 (2005), 296320. doi: 10.1016/j.jmaa.2004.09.027. Google Scholar 
[16] 
S. E. A. Mohammed, "Stochastic Functional Differential Equations," Research Notes in Mathematics, 99, Pitman (Advanced Publishing Program), Boston, MA, 1984. Google Scholar 
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