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In mathematics probability theory, a basic affine jump diffusion is a stochastic process Z of the form
where B {\displaystyle B} is a standard Brownian motion, and J {\displaystyle J} is an independent compound Poisson process with constant jump intensity l {\displaystyle l} and independent exponentially distributed jumps with mean μ {\displaystyle \mu }. For the process to be well defined, it is necessary that κ θ ≥ 0 {\displaystyle \kappa \theta \geq 0} and μ ≥ 0 {\displaystyle \mu \geq 0}. A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross process is a special case of a basic AJD.
Basic AJDs are attractive for modeling default times in credit risk applications, since both the moment generating function
and the characteristic function