The present study utilizes the Girsanov transformation based framework for solving a nonlinear stochastic dynamical system in an efficient way in comparison to other available approximate methods. In this approach, a rejection sampling is formulated to evaluate the Radon-Nikodym derivative arising from the change of measure due to Girsanov transformation. The rejection sampling is applied on the Euler Maruyama approximated sample paths which draw exact paths independent of the diffusion dynamics of the underlying dynamical system. The efficacy of the proposed framework is ensured using more accurate numerical as well as exact nonlinear methods. Finally, nonlinear applied test problems are considered to confirm the theoretical results. The test problems demonstrates that the proposed exact formulation of the Euler-Maruyama provides an almost exact approximation to both the displacement and velocity states of a second order non-linear dynamical system.
翻译:本研究利用Girsanov变换框架,与其他现有近似方法相比,以有效的方式解决非线性随机动态系统问题,采用Girsanov变换框架,以有效方式解决非线性随机动态系统问题;在这种方法中,为评价Girsanov变换所导致测量变化产生的Radon-Nikodym衍生物,制定了拒绝取样方法;在Euler Maruyama近似采样路径上应用拒绝取样方法,这些途径与基本动态系统的传播动态不相干,得出精确路径;用更准确的数字和精确的非线性方法确保拟议框架的效力;最后,考虑非线性应用测试问题,以证实理论结果;测试问题表明,Euler-Maruyama的拟议精确配制提供了几乎准确的近似于第二顺序非线性动态系统外移和速度状态的近似近。