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71.
Andreas Rößler 《BIT Numerical Mathematics》2006,46(1):97-110
A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance. 相似文献
72.
在局部凸空间中考虑集值优化问题(VP)在强有效解意义下的Kuhn-Tucker最优性条件.在近似锥.次类凸假设下利用择一性定理得到了(VP)取得强有效解的必要条件,利用基泛函的性质给出了(VP)取得强有效解的充分条件,最后给出了一种与(VP)等价的无约束规划。 相似文献
73.
Andreas Rößler 《BIT Numerical Mathematics》2007,47(3):657-680
The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main
novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due
to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with
order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly.
AMS subject classification (2000) 65C30, 65L06, 60H35, 60H10 相似文献
74.
We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals. 相似文献
75.
Empirical minimization 总被引:3,自引:0,他引:3
We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing
the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large
numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the
empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp.
The method of proof we use is based on Talagrand's concentration inequality for empirical processes.
Research partially supported by NSF under award DMS-0434393.
Research partially supported by the Australian Research Council Discovery Porject DP0343616. 相似文献
76.
Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms 总被引:2,自引:0,他引:2
Hoang Tuy 《Journal of Global Optimization》1991,1(1):23-36
We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions. 相似文献
77.
78.
??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation. 相似文献
79.
Alexander Ya. Kruger 《Set-Valued Analysis》2006,14(2):187-206
The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains
a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection
of sets to be regular. 相似文献
80.
We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process. 相似文献