An averaging principle for a completely integrable stochastic Hamiltonian system
An averaging principle for a completely integrable stochastic Hamiltonian system
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DOI：
10.1088/0951-7715/21/4/008
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发表时间：
2008-04
期刊：
影响因子：
1.7
通讯作者：
Xue-Mei Li
中科院分区：
文献类型：
--
作者：
Xue-Mei Li
我们研究了ϵ阶小横截扰动对完全可积随机哈密顿系统的有效行为，这里我们指的是扩散向量场由完全可积的哈密顿函数族Hi，i=1，…构成的随机微分方程证明了平均化原理成立，并且当时间重定标为1/ϵ→时，解的作用分量收敛于确定性微分方程组的解，如ϵ0。给出了收敛速度的估计。当摄动是哈密顿向量场时，极限确定性系统是常数的，在这种情况下，我们证明了在1/ϵ2尺度上的解的作用分量收敛于极限随机可微方程的作用分量。
We investigate the effective behaviour of a small transversal perturbation of order ϵ to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic differential equation whose diffusion vector fields are formed from a completely integrable family of Hamiltonian functions Hi, i = 1, …, n. An averaging principle is shown to hold and the action component of the solution converges, as ϵ → 0, to the solution of a deterministic system of differential equations when the time is rescaled at 1/ϵ. An estimate for the rate of the convergence is given. In the case when the perturbation is a Hamiltonian vector field, the limiting deterministic system is constant in which case we show that the action component of the solution scaled at 1/ϵ2 converges to that of a limiting stochastic differentiable equation.