The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Robert J Elliott - One of the best experts on this subject based on the ideXlab platform.
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multiple solutions to stochastic differential delay equations and a related Comparison Theorem
Stochastic Analysis and Applications, 2013Co-Authors: Zhe Yang, Lifeng Wei, Robert J ElliottAbstract:In this article, we discuss the existence of multiple solutions to a one-dimensional stochastic differential delay equation with continuous drift coefficients and derive a related Comparison Theorem.
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a converse Comparison Theorem for anticipated bsdes and related non linear expectations
Stochastic Processes and their Applications, 2013Co-Authors: Robert J Elliott, Zhe YangAbstract:Abstract The converse Comparison Theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such Theorem has been proved for anticipated BSDEs. In this paper, we derive a converse Comparison Theorem by first giving an existence and uniqueness Theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to ( f , δ ) -expectations induced by anticipated BSDEs.
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a general Comparison Theorem for backward stochastic differential equations
Advances in Applied Probability, 2010Co-Authors: Samuel N Cohen, Robert J Elliott, Charles E M PearceAbstract:A useful result when dealing with backward stochastic differential equations is the Comparison Theorem of Peng (1992). When the equations are not based on Brownian motion, the Comparison Theorem no longer holds in general. In this paper we present a condition for a Comparison Theorem to hold for backward stochastic differential equations based on arbitrary martingales. This Theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectations are also explored.
Chenggui Yuan - One of the best experts on this subject based on the ideXlab platform.
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Comparison Theorem for distribution dependent neutral sfdes
Journal of Evolution Equations, 2021Co-Authors: Xing Huang, Chenggui YuanAbstract:In this paper, the existence and uniqueness of strong solutions to distribution-dependent neutral SFDEs are proved. We give the conditions such that the order preservation of these equations holds. Moreover, we show these conditions are also necessary when the coefficients are continuous. Under sufficient conditions, the result extends the one in the distribution-independent case, and the necessity of these conditions is new even in distribution-independent case.
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Comparison Theorem for stochastic differential delay equations with jumps
arXiv: Probability, 2011Co-Authors: Jianhai Bao, Chenggui YuanAbstract:In this paper we establish a Comparison Theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the Comparison Theorem need not hold whenever the diffusion term contains a delay function although the jump-diffusion coefficient could contain a delay function. Moreover, another example is established to show that the Comparison Theorem is not necessary to be true provided that the jump-diffusion term is non-increasing with respect to the delay variable.
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Comparison Theorem of one dimensional stochastic hybrid delay systems
Systems & Control Letters, 2008Co-Authors: Zhe Yang, Xuerong Mao, Chenggui YuanAbstract:The Comparison Theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the Comparison Theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems.
Zhe Yang - One of the best experts on this subject based on the ideXlab platform.
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multiple solutions to stochastic differential delay equations and a related Comparison Theorem
Stochastic Analysis and Applications, 2013Co-Authors: Zhe Yang, Lifeng Wei, Robert J ElliottAbstract:In this article, we discuss the existence of multiple solutions to a one-dimensional stochastic differential delay equation with continuous drift coefficients and derive a related Comparison Theorem.
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a converse Comparison Theorem for anticipated bsdes and related non linear expectations
Stochastic Processes and their Applications, 2013Co-Authors: Robert J Elliott, Zhe YangAbstract:Abstract The converse Comparison Theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such Theorem has been proved for anticipated BSDEs. In this paper, we derive a converse Comparison Theorem by first giving an existence and uniqueness Theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to ( f , δ ) -expectations induced by anticipated BSDEs.
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Comparison Theorem of one dimensional stochastic hybrid delay systems
Systems & Control Letters, 2008Co-Authors: Zhe Yang, Xuerong Mao, Chenggui YuanAbstract:The Comparison Theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the Comparison Theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems.
Charles E M Pearce - One of the best experts on this subject based on the ideXlab platform.
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a general Comparison Theorem for backward stochastic differential equations
Advances in Applied Probability, 2010Co-Authors: Samuel N Cohen, Robert J Elliott, Charles E M PearceAbstract:A useful result when dealing with backward stochastic differential equations is the Comparison Theorem of Peng (1992). When the equations are not based on Brownian motion, the Comparison Theorem no longer holds in general. In this paper we present a condition for a Comparison Theorem to hold for backward stochastic differential equations based on arbitrary martingales. This Theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectations are also explored.
Shige Peng - One of the best experts on this subject based on the ideXlab platform.
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Comparison Theorem feynman kac formula and girsanov transformation for bsdes driven by g brownian motion
Stochastic Processes and their Applications, 2014Co-Authors: Mingshang Hu, Shige Peng, Shaolin Ji, Yongsheng SongAbstract:In this paper, we study Comparison Theorem, nonlinear Feynman–Kac formula and Girsanov transformation of the following BSDE driven by a G-Brownian motion: Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt), where K is a decreasing G-martingale.
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Comparison Theorem feynman kac formula and girsanov transformation for bsdes driven by g brownian motion
arXiv: Probability, 2012Co-Authors: Mingshang Hu, Shige Peng, Shaolin Ji, Yongsheng SongAbstract:In this paper, we study Comparison Theorem, nonlinear Feynman-Kac formula and Girsanov transformation of the BSDE driven by a G-Brownian motion.
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on the Comparison Theorem for multidimensional bsdes
Comptes Rendus Mathematique, 2006Co-Authors: Shige PengAbstract:Abstract In this Note, we give a necessary and sufficient condition under which the Comparison Theorem holds for multidimensional backward stochastic differential equations (BSDEs) and for matrix-valued BSDEs. To cite this article: Y. Hu, S. Peng, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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necessary and sufficient condition for Comparison Theorem of 1 dimensional stochastic differential equations
Stochastic Processes and their Applications, 2006Co-Authors: Shige Peng, Xuehong ZhuAbstract:Abstract In this paper, we present a new approach to obtain the Comparison Theorem of two 1-dimensional SDEs with diffusion and jumps. The two equations is treated as one two-dimensional SDE and the Comparison requirement is regarded as to keep the solution ( X t 1 , X t 2 ) within the constraint K = { ( x 1 , x 2 ) ; x 1 ⩽ x 2 } . We then apply a new criteria of “viability condition” which is a necessary and sufficient condition to keep the solution to be inside the constraint K.
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a general converse Comparison Theorem for backward stochastic differential equations
Comptes Rendus De L Academie Des Sciences Serie I-mathematique, 2001Co-Authors: Francois Coquet, Jean Memin, Shige PengAbstract:Abstract In this Note, we establish a general converse Comparison Theorem for backward stochastic differential equations (BSDEs).