In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condi...In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condition.As an application,we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.展开更多
In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.
Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the...Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.展开更多
In this paper, we deal with one dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.
In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations （BDSDEs） with coefficients left-Lipschitz in y （may be discontinuous） and Lipschitz in z is studied. Als...In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations （BDSDEs） with coefficients left-Lipschitz in y （may be discontinuous） and Lipschitz in z is studied. Also, the associated comparison theorem is obtained.展开更多
In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an exis...In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs.展开更多
A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which al...A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.展开更多
In this paper we consider infinite horizon backward doubly stochastic differential equations （BDS- DEs for short） coupled with forward stochastic differential equations, whose terminal functions are non-degenerate. ...In this paper we consider infinite horizon backward doubly stochastic differential equations （BDS- DEs for short） coupled with forward stochastic differential equations, whose terminal functions are non-degenerate. For such kind of BDSDEs, we study the existence and uniqueness of their solutions taking values in weighted Lp（dx）¤L2（dx）space （p _〉 2）, and obtain the stationary property for the solutions.展开更多
We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal...We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.展开更多
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It?-Kunita integral. By the application of this theorem, ...This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It?-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.展开更多
In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipsc...In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function <em>f</em><sub><em>n</em></sub> to the coefficient <em>f</em>, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.展开更多
In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochast...In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochastic Lipschitz condition and obtain the related comparison theorem.Besides,the authors further relax the conditions and deduce the existence theorem of solutions under stochastic linear growth and continuous conditions,and the authors also prove the associated comparison theorem.Finally,an asset pricing problem is discussed,which demonstrates the application of the general meanfield BDSDEs in finance.展开更多
In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first...In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.展开更多
In this paper,the authors establish the existence and uniqueness theorem of L^(p)(1<p≤2)solutions for multidimensional backward doubly stochastic differential equations(BDSDEs for short)under the p-order globally(...In this paper,the authors establish the existence and uniqueness theorem of L^(p)(1<p≤2)solutions for multidimensional backward doubly stochastic differential equations(BDSDEs for short)under the p-order globally(locally)weak monotonicity conditions.Comparison theorem of L^(p) solutions for one-dimensional BDSDEs is also proved.These conclusions unify and generalize some known results.展开更多
基金supported by Beijing Natural Science Foundation(No.1222004)Yuyou Project of North University of Technology(No.207051360020XN140/007)Scientific Research Foundation of North University of Technology(No.110051360002)。
文摘In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condition.As an application,we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.
基金Supported by Marie Curie Initial Training Network (Grant No. PITN-GA2008-213841)National Basic Research Program of China (973 Program, No. 2007CB814906)
文摘In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.
基金supported by the National Natural Science Foundation of China (Nos. 10771122,11071145)the Shandong Provincial Natural Science Foundation of China (No. Y2006A08)+2 种基金the Foundation for Innovative Research Groups of National Natural Science Foundation of China (No. 10921101)the National Basic Research Program of China (the 973 Program) (No. 2007CB814900)the Independent Innovation Foundation of Shandong University (No. 2010JQ010)
文摘Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.
基金supported by the Young Scholar Award for Doctoral Students of the Ministry of Education of China, the Marie Curie Initial Training Network(PITN-GA-2008-213841)the National Basic Research Program of China(973 Program,No.2007CB814904)+3 种基金the National Natural Science Foundations of China(No.10921101)Shandong Province(No.2008BS01024)the Science Fund for Distinguished Young Scholars of Shandong Province(No.JQ200801)Shandong University(No.2009JQ004)
文摘In this paper, we deal with one dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.
基金Supported by the National Natural Science Foundation of China(Nos.11371226,11071145,11301298,11201268 and 11231005)Foundation for Innovative Research Groups of National Natural Science Foundation of China(No.11221061)+1 种基金the 111 Project(No.B12023)Natural Science Foundation of Shandong Province of China(ZR2012AQ013)
文摘In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations （BDSDEs） with coefficients left-Lipschitz in y （may be discontinuous） and Lipschitz in z is studied. Also, the associated comparison theorem is obtained.
基金Supported by Chinese Natural Science Foundation(Grant No.11271093)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090002110047)
文摘In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs.
基金supported by TWAS Research Grants to individuals (No. 09-100 RG/MATHS/AF/AC-IUNESCO FR: 3240230311)
文摘A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11126081,11101090,11401212 and 11471079the Fundamental Research Funds for the Central Universities under Grant No.WM1014032
文摘In this paper we consider infinite horizon backward doubly stochastic differential equations （BDS- DEs for short） coupled with forward stochastic differential equations, whose terminal functions are non-degenerate. For such kind of BDSDEs, we study the existence and uniqueness of their solutions taking values in weighted Lp（dx）¤L2（dx）space （p _〉 2）, and obtain the stationary property for the solutions.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11871309,11671229,71871129,11371226,11301298)the National Key R&D Program of China(Grant No.2018 YFA0703900)+2 种基金the Natural Science Foundation of Shandong Province(No.ZR2019MA013)the Special Funds of Taishan Scholar Project(No.tsqn20161041)the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.
文摘We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.
基金supported by the National Natural Science Foundation of China (10726075)
文摘This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It?-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
文摘In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function <em>f</em><sub><em>n</em></sub> to the coefficient <em>f</em>, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.
基金supported by the Zhiyuan Science Foundation of BIPT under Grant No.2024212National Key R&D Program of China under Grant No.2018YFA0703900+1 种基金the National Natural Science Foundation of China under Grant Nos.11871309 and 11371226Natural Science Foundation of Shandong Province under Grant No.ZR2020QA026.
文摘In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochastic Lipschitz condition and obtain the related comparison theorem.Besides,the authors further relax the conditions and deduce the existence theorem of solutions under stochastic linear growth and continuous conditions,and the authors also prove the associated comparison theorem.Finally,an asset pricing problem is discussed,which demonstrates the application of the general meanfield BDSDEs in finance.
基金supported in part by the NSF of P.R.China(11871037,11222110)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.
基金supported by the National Natural Science Foundation of China(No.11601509).
文摘In this paper,the authors establish the existence and uniqueness theorem of L^(p)(1<p≤2)solutions for multidimensional backward doubly stochastic differential equations(BDSDEs for short)under the p-order globally(locally)weak monotonicity conditions.Comparison theorem of L^(p) solutions for one-dimensional BDSDEs is also proved.These conclusions unify and generalize some known results.
