This paper is concerned with the stochastically stability for the m-dimensional linear stochastic differential equations with respect to fractional Brownian motion （FBM） with Hurst parameter H ∈ （1/2, 1）. On the ...This paper is concerned with the stochastically stability for the m-dimensional linear stochastic differential equations with respect to fractional Brownian motion （FBM） with Hurst parameter H ∈ （1/2, 1）. On the basis of the pioneering work of Duncan and Hu, a Ito＇s formula is given. An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.展开更多
This paper gives the necessary condition and one sufficient condition of the quasimonotonic function, and proves that the linear fractional function is quasi-monotone.
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any...A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.展开更多
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI...The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.展开更多
基金Natural Science Foundation of Shanghai,China(No.07ZR14002)
文摘This paper is concerned with the stochastically stability for the m-dimensional linear stochastic differential equations with respect to fractional Brownian motion （FBM） with Hurst parameter H ∈ （1/2, 1）. On the basis of the pioneering work of Duncan and Hu, a Ito＇s formula is given. An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.
文摘This paper gives the necessary condition and one sufficient condition of the quasimonotonic function, and proves that the linear fractional function is quasi-monotone.
基金supported by the National Science Foundation of USA(Grant Nos.1522629 and 1522654)the Office of Naval Research of USA(Grant Nos.N00014-11-1-0068 and N00014-15-12048)+1 种基金the Air Force Research Laboratory of USA(Contract No.FA8651-08-D-0108/0054)National Natural Science Foundation of China(Grant No.11571178)
文摘A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.
基金supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137)the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217)the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)
文摘The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.
