The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a ...The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.展开更多
This paper formulates and studies a delayed ehemostat with Levy noises.Existence of the glohally positive solution is proved first by establishing suitable Lyapunov functions,and a further result on exact Lyapunov exp...This paper formulates and studies a delayed ehemostat with Levy noises.Existence of the glohally positive solution is proved first by establishing suitable Lyapunov functions,and a further result on exact Lyapunov exponent shows the growth of the total concentration in the ehemostat.Then,we prove existence of the uniquely ergodic stationary distribution for a subsystem of the nutrient,based on this,a unique threshold is identified,which completely determines persistence or not of the microorganism in the ehemostat.Besides,recurrence is studied under special conditions in case that the microorganism persists.Results indicate that all the noises have negative effects on persistence of the microorganism,and the time delay has almost no effects on the sample Lyapunov exponent and the threshold value of the ehemostat.展开更多
In this paper,we establish a large deviation principle for two-dimensional primitive equations driven by multiplicative Lévy noises.The proof is based on the weak convergence approach.
基金supported by National Natural Science Foundation of China (Grant No. 11101090, 11101140, 10771122)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090071120002)+2 种基金Innovation Team Foundation of the Department of Education of Zhejiang Province (Grant No. T200924)Natural Science Foundation of Zhejiang Province (Grant No. Y6110775, Y6110789)Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.
文摘This paper formulates and studies a delayed ehemostat with Levy noises.Existence of the glohally positive solution is proved first by establishing suitable Lyapunov functions,and a further result on exact Lyapunov exponent shows the growth of the total concentration in the ehemostat.Then,we prove existence of the uniquely ergodic stationary distribution for a subsystem of the nutrient,based on this,a unique threshold is identified,which completely determines persistence or not of the microorganism in the ehemostat.Besides,recurrence is studied under special conditions in case that the microorganism persists.Results indicate that all the noises have negative effects on persistence of the microorganism,and the time delay has almost no effects on the sample Lyapunov exponent and the threshold value of the ehemostat.
基金This work is partly supported by BJNSF(No.1212008)National Natural Science Foundation of China(No.11801032,12171032,11971227,12071123)Beijing Institute of Technology Research Fund Program for Young Scholars and Key Laboratory of Mathematical Theory and Computation in Information Security.
文摘In this paper,we establish a large deviation principle for two-dimensional primitive equations driven by multiplicative Lévy noises.The proof is based on the weak convergence approach.
