AN ASYMPTOTIC THEORY FOR JUMP DIFFUSION MODELS
为具有良好尺度函数的循环跳跃扩散模型建立渐近理论，涵盖非平稳和平稳情形，发现平稳时极限分布为正态，非平稳时则为广义扩散过程。
This paper presents an asymptotic theory for recurrent jump diffusion models with well-defined scale functions. The class of such models is broad, including general nonstationary as well as stationary jump diffusions with state-dependent jump sizes and intensities. The asymptotics for recurrent jump diffusion models with scale functions are largely comparable to the asymptotics for the corresponding diffusion models without jumps. For stationary jump diffusions, our asymptotics yield the usual law of large numbers and the standard central limit theory with normal limit distributions. The asymptotics for nonstationary jump diffusions, on the other hand, are nonstandard and the limit distributions are given as generalized diffusion processes.