论文标题
在Marcus意义上的Hamiltonian随机微分方程的符号方法
Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus
论文作者
论文摘要
在MARCUS的意义上，一类具有乘法lévy噪声的汉密尔顿随机微分方程，并考虑了Symbletice Euler方案的构建和数值实现方法。设计了这种哈密顿随机微分方程的一般符号欧拉方案，并证明了其收敛定理。第二部分详细介绍了该方案的可实现数值实现方法。进行了一些数值实验，以通过长时间间隔在其轨道，hamlitonian和收敛顺序的模拟中证明所提出方法的有效性和优越性。
A class of Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus, and the construction and numerical implementation methods of symplectic Euler scheme, are considered. A general symplectic Euler scheme for this kind of Hamiltonian stochastic differential equations is devised, and its convergence theorem is proved. The second part presents realizable numerical implementation methods for this scheme in details. Some numerical experiments are conducted to demonstrate the effectiveness and superiority of the proposed method by the simulations of its orbits, Hamlitonian,and convergence order over a long time interval.
