Basic affine jump diffusion

In probability theory, a basic affine jump diffusion (basic AJD) is a stochastic process Z of the form where is a standard Brownian motion, and is an independent compound Poisson process with constant jump intensity and independent exponentially distributed jumps with mean . For the process to be well defined, it is necessary that and . A basic AJD is a special case of an and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD. and the characteristic function are known in closed form.

Basic affine jump diffusion

In probability theory, a basic affine jump diffusion (basic AJD) is a stochastic process Z of the form where is a standard Brownian motion, and is an independent compound Poisson process with constant jump intensity and independent exponentially distributed jumps with mean . For the process to be well defined, it is necessary that and . A basic AJD is a special case of an and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD. and the characteristic function are known in closed form.