Multivalued Stochastic Differential Equations with Non-Lipschitz Coeffcients
Multivalued Stochastic Differential Equations with Non-Lipschitz Coeffcients
摘要
The existence and uniqueness of solutions to the multivalued stochastic differential equations with non-Lipschitz coefficients are proved, and bicontinuous modifications of the solutions are obtained.
基金
supported by the National Natural Science Foundation of China (No.10871215).
参考文献11
-
1Toshio Yamada,Yukio Ogura.On the strong comparison theorems for solutions of stochastic differential equations[J].Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete.1981(1)
-
2Zhang,X,Zhu,J.Non-Lipschitz stochastic di-erential equations driven by multi-parameter Brownian motions[].StochDyn.2006
-
3Aubin,J.P.,Cellina,A.Di-erential Inclusions[].GrundMathWiss.1984
-
4Brezis,H.Op′erateurs Maximaux Monotones et Semi-Groups de Contractions dans les Espaces de Hilbert[]..1973
-
5C′epa,E.E′quations di-′erentielles stochastiques multivoques[].S′eminProbab.1995
-
6Lamarque,C -H,Bernardin,F,Bastien,J.Study of a rheological model with a friction term and a cubic team:deterministic and stochastic cases[].EurJMechA Solids.2004
-
7Le Gall,J.F.Applications du temps local aux ′equations di-′erentielles stochastiques unidimensionnelles[].S′eminProbab.1983
-
8L′epingle,D,Marois,C.Equations di-rentielles stochastiques multivoques unidimensionnelles[].S′emin Probab.1987
-
9Revuz,D.,Yor,M.Continuous Martingales and Brownian Motion[].GrundMathWiss.1991
-
10Ren J,Zhang X.Stochastic flows for SDEs with non-Lipschitz coefficients[].Bulletin des Sciences Mathematiques.2003
-
1LI Zhi,LUO Jiaowan.Neutral Functional Partial Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients[J].Journal of Partial Differential Equations,2014,27(1):50-63. 被引量:1
-
2乔会杰.HOMEOMORPHISM FLOWS FOR NON-LIPSCHITZ SDES DRIVEN BY LVY PROCESSES[J].Acta Mathematica Scientia,2012,32(3):1115-1125.
-
3Ji Cheng LIU.Rate of Convergence of Euler's Approximations for SDEs with Non-Lipschitz Coefficients[J].Acta Mathematica Sinica,English Series,2013,29(8):1555-1568. 被引量:1
-
4ZHAO Shoujiang,GAO Fuqing School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China.A Necessary Condition on Comparison Theorem for One-Dimensional Stochastic Differential Equation[J].Wuhan University Journal of Natural Sciences,2010,15(1):13-15.
-
5Jing WU.On Wiener-Poisson Type Multivalued Stochastic Differential Equations with Non-Lipschitz Coefficients[J].Acta Mathematica Sinica,English Series,2013,29(4):675-690. 被引量:2
-
6Weiyin Fei School of Math. and Physics, Anhui University of Technology and Science,Wuhu 241000, Anhui.RELATIONS BETWEEN SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SEMIMARTINGALE WITH NON-LIPSCHITZ COEFFICIENTS[J].Annals of Differential Equations,2010,26(1):16-23. 被引量:1
-
7LU Min,WANG Zeng-wu.A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient[J].Chinese Quarterly Journal of Mathematics,2009,24(4):568-573.
-
8Wei Yin FEI.On Small Time Large Deviation Principle for Diffusion Processes on Hilbert Spaces under Non-Lipschitzian Condition[J].Journal of Mathematical Research and Exposition,2011,31(1):142-146.
-
9Guangqiang LAN.Large deviation principle of stochastic differential equations with non-Lipschitzian coefficients[J].Frontiers of Mathematics in China,2013,8(6):1307-1321.
-
10Li Juan SHEN,Ji Tao SUN.Global Existence of Solutions for Stochastic Impulsive Differential Equations[J].Acta Mathematica Sinica,English Series,2011,27(4):773-780. 被引量:1