Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to approximations in inference. In this paper, we give the first general collection of methodologies for exact (in this context meaning discretisation-free) likelihood-based inference for discretely observed finite activity jump-diffusions. The only sources of error involved are Monte Carlo error and convergence of EM or MCMC algorithms. We shall introduce both frequentist and Bayesian approaches, illustrating the methodology through simulated and real examples.

翻译：离散观测的跳跃扩散过程的统计推论是一个复杂的问题,引发新的方法挑战,因此,现有方法总是采用时间分解法,不可避免地导致推理近似值。在本文中,我们首先对离散观测的有限活动跳跃扩散的精确(此处指无离散)概率推论进行了一般性汇编。唯一的错误来源是蒙特卡洛错误以及EM或MCMC算法的趋同。我们将采用常住和巴耶斯两种方法,通过模拟和真实的例子来说明该方法。