论文标题
渐近膨胀，用于由伽马过程驱动的随机微分方程的过渡密度
Asymptotic expansion for the transition densities of stochastic differential equations driven by the gamma processes
论文作者
论文摘要
在本文中，由Li（2013b）和Li and Chen（2016）开发的渐近扩展方法的开明，我们提出了由伽马过程驱动的随机微分方程（SDES）过渡密度的泰勒型近似，这是一种特殊类型的征费过程。在将过渡密度表示为作用于相关SDE解决方案的Dirac Delta函数的有条件期望之后，提出了计算多个随机积分期望在伽马过程中有条件条件的关键技术方法。为了测试我们方法的效率，我们检查了纯跳跃Ornstein-Uhlenbeck（OU）模型及其扩展到两个跳跃模型。对于每个模型，我们近似的过渡密度与通过特征函数的反傅立叶变换获得的基准密度之间的最大相对误差足够小，这表明了我们近似方法的效率。
In this paper, enlightened by the asymptotic expansion methodology developed by Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by the gamma processes, a special type of Levy processes. After representing the transition density as a conditional expectation of Dirac delta function acting on the solution of the related SDE, the key technical method for calculating the expectation of multiple stochastic integrals conditional on the gamma process is presented. To numerically test the efficiency of our method, we examine the pure jump Ornstein--Uhlenbeck (OU) model and its extensions to two jump-diffusion models. For each model, the maximum relative error between our approximated transition density and the benchmark density obtained by the inverse Fourier transform of the characteristic function is sufficiently small, which shows the efficiency of our approximated method.
