带跳跃扩散的自适应弱逼近方法
Adaptive Weak Approximation of Diffusions with Jumps
AI总结：
针对带跳跃的随机微分方程的弱逼近问题，提出基于随机流和对偶后验误差展开的蒙特卡洛欧拉自适应时间步长方法，并验证其有效性。
摘要：
本文针对带跳跃扩散的随机微分方程的弱逼近问题，发展了蒙特卡洛欧拉自适应时间步长方法。主要结果是基于随机流和离散对偶后向问题，推导出计算误差的新展开式，其可计算的前导项具有后验形式，扩展了[STZ]中的结果。这些展开式能够高效、准确地计算误差估计。描述了随机时间步长或拟确定性时间步长的自适应算法。数值算例展示了所提出的误差逼近和自适应时间步长方法的性能。
英文摘要：
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples show the performance of the proposed error approximation and of the described adaptive time-stepping methods.
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