In-Probability Approximation and Simulation of Nonlinear Jump-Diffusion Stochastic Differential Equations
In-Probability Approximation and Simulation of Nonlinear Jump-Diffusion Stochastic Differential Equations
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DOI：
10.1093/imamci/4.1.65
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发表时间：
1987
影响因子：
1.5
通讯作者：
Y. Maghsoodi;C. Harris
中科院分区：
文献类型：
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作者：
Y. Maghsoodi;C. Harris
研究了一类同时受Wiener过程和非齐次Poisson过程驱动的Itôstochastic微分方程的数值解问题。该方程可作为受脉冲型随机干扰和白色噪声影响的系统的模型。离散化和泰勒展开的方法被用来与一个“不可能”的标准误差测量。给出了确定随机截断误差阶数的误差分析定理。这个定理评估了以前类似的工作中的特殊情况下，没有跳跃组件是本，以及提供的跳跃扩散过程的近似准则的结果。对于后者的情况下，它表明，通过这种方法，不像无跳的情况下，误差可以改善的基本随机柯西-欧拉格式的总误差的加法分量的阶数增加的程度。一阶算法与此属性推导和结果的收敛速度的两个计划和可计算的评估，实施和模拟。仿真结果表明，该算法在稳定性和效率上明显优于基本方案。
The problem of numerical solution of a wide class of Itôstochastic differential equations simultaneously driven by Wiener and inhomogeneous Poisson processes is considered. The equations serve as models for systems affected by random disturbances of impulsive type as well as white noise. The method of discretization and Taylor expansion is used in conjunction with an ‘in-probability’ criterion for error measurement. An error-analysis theorem determining the orders of the stochastic truncation errors is presented. This theorem assesses the results of previous similar work in the special case where no jump component is present, as well as providing guidelines for the approximation of the jump-diffusion processes. For the latter case it is shown that, via this approach and unlike the no-jump case, the error can be improved over that of the basic stochastic Cauchy-Euler scheme only to the extent of increasing the order of an additive component of the total error.A first-order algorithm with this property is derived and results on the rate of convergence of both schemes and computable evaluations, implementation, and simulations are presented. Simulation results demonstrate significant superiority of the proposed algorithm over the basic scheme in stability and efficiency.