This paper is interested in solving a multidimensional backward stochastic differential equation （BSDE） whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence...This paper is interested in solving a multidimensional backward stochastic differential equation （BSDE） whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results.展开更多
We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition...We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.展开更多
The authors consider the multidimensional aggregation equation tp-div（p K＊ ρ） = 0 in which the radially symmetric attractive interaction kernel has a mild singularity at the origin （Lipschitz or better）, and rev...The authors consider the multidimensional aggregation equation tp-div（p K＊ ρ） = 0 in which the radially symmetric attractive interaction kernel has a mild singularity at the origin （Lipschitz or better）, and review recent results on this problem concerning well-posedness of nonnegative solutions and finite time blowup in multiple space dimensions depending on the behavior of the kernel at the origin. The problem with bounded initial data, data in L^p ∩ L^1, and measure solutions are also considered.展开更多
基金The authors would like to thank the anonymous referees for their careful reading and helpful suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11101422）, the Fundamental Research Funds for the Central Universities （Grant No. 2012QNA36）, and Qing Lan Project.
文摘This paper is interested in solving a multidimensional backward stochastic differential equation （BSDE） whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results.
基金Supported by National Natural Science Foundation of China(Grant No.11371362)the Fundamental Research Funds for the Central Universities(Grant No.2012QNA36)
文摘We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.
基金Project supported by the Office of Naval Research,the Army Research Office and the National Science Foundation (No.DMS-0907931)
文摘The authors consider the multidimensional aggregation equation tp-div（p K＊ ρ） = 0 in which the radially symmetric attractive interaction kernel has a mild singularity at the origin （Lipschitz or better）, and review recent results on this problem concerning well-posedness of nonnegative solutions and finite time blowup in multiple space dimensions depending on the behavior of the kernel at the origin. The problem with bounded initial data, data in L^p ∩ L^1, and measure solutions are also considered.
